Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D97 | C2 | semidirect |
| 2. C23×D388 | C2 | semidirect |
| 3. C23×C22⋊D97 | C2 | semidirect |
| 4. C2×#15690780 | C2 | direct (N × H) |
| 5. C22×#13095488 | C2 | semidirect |
| 6. C22×C22⋊C4×C97 | C2 | semidirect |
| 10. C24×D97 | C22 | semidirect |
| 11. C24×D97 | C22 | semidirect |
| 13. C22×D388 | C22 | semidirect |
| 15. C22×C22⋊D97 | C22 | semidirect |
| 16. C23×Dic97 | C22 | semidirect |
| 17. #15690780 | C22 | direct (N × H) |
| 18. C2×#13095488 | C22 | semidirect |
| 20. C23×C4×C97 | C22 | semidirect |
| 21. C2×C22⋊C4×C97 | C22 | semidirect |
| 29. C23×D97 | D4 | semidirect |
| 31. C23×D97 | C23 | semidirect |
| 32. C23×D97 | C23 | semidirect |
| 34. C2×D388 | C23 | semidirect |
| 36. C2×C22⋊D97 | C23 | semidirect |
| 38. C22×Dic97 | C23 | semidirect |
| 39. #13095488 | C23 | semidirect |
| 41. C24×C97 | D4 | semidirect |
| 45. C22×C4×C97 | C23 | semidirect |
| 46. C22⋊C4×C97 | C23 | semidirect |
| 51. C23×C97 | C2×D4 | semidirect |
| 63. C22×D97 | C2×D4 | semidirect |
| 65. C22×D97 | C24 | semidirect |
| 67. C2×C4×C97 | C24 | semidirect |
| 70. C2×Dic97 | C24 | semidirect |
| 74. C22×C97 | #120 | semidirect |
| 77. C22×C97 | C22×D4 | semidirect |
| 86. C2×D97 | C22×D4 | semidirect |
| 90. C2×C97 | C2×#120 | semidirect |
| 96. C97 | C22×#120 | semidirect |
| 102. C22×C22⋊C4 | D97 | semidirect |
| 114. C23×C4 | C2×D97 | semidirect |
| 117. C2×C22⋊C4 | C2×D97 | semidirect |
| 130. C24 | D388 | semidirect |
| 140. C22×C4 | C22×D97 | semidirect |
| 142. C22⋊C4 | C22×D97 | semidirect |
| 159. C23 | C2×D388 | semidirect |
| 167. C2×C4 | C23×D97 | semidirect |
| 178. C22 | #15690780 | direct (N × H) |
| 181. C22 | C22×D388 | semidirect |
| 188. C2 | C2×#15690780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D97 | 2 |
| C23×D388 | 2 |
| C23×C22⋊D97 | 2 |
| C2×#15690780 | 2 |
| C22×#13095488 | 2 |
| C22×C22⋊C4×C97 | 2 |
| C22×#120 | 97 |