Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
4632 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1106 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. C24×#87604 | C2 | semidirect |
| 2. C22×C22⋊#87604 | C2 | direct (N × H) |
| 5. C23×#87604 | C22 | semidirect |
| 6. C2×C22⋊#87604 | C22 | direct (N × H) |
| 8. C24×D97 | C4 | semidirect |
| 9. C24×D97 | C4 | semidirect |
| 12. C25×C97 | C4 | semidirect |
| 14. C22×#87604 | C23 | semidirect |
| 15. C22⋊#87604 | C23 | direct (N × H) |
| 20. C23×D97 | C2×C4 | semidirect |
| 21. C23×D97 | C2×C4 | semidirect |
| 27. C24×C97 | C2×C4 | semidirect |
| 29. C23×C97 | C22⋊C4 | semidirect |
| 31. C23×C97 | C22×C4 | semidirect |
| 35. C22×D97 | C22⋊C4 | semidirect |
| 37. C22×D97 | C22×C4 | semidirect |
| 38. C22×D97 | C22×C4 | semidirect |
| 43. C2×#87604 | C24 | semidirect |
| 45. C22×C97 | C2×C22⋊C4 | semidirect |
| 47. C22×C97 | C23×C4 | semidirect |
| 51. C2×D97 | C2×C22⋊C4 | semidirect |
| 53. C2×D97 | C23×C4 | semidirect |
| 58. C2×C97 | C22×C22⋊C4 | semidirect |
| 61. D97 | C22×C22⋊C4 | semidirect |
| 64. C97 | C23×C22⋊C4 | semidirect |
| 73. C25 | #87604 | semidirect |
| 88. C24 | C2×#87604 | semidirect |
| 103. C23 | C22⋊#87604 | direct (N × H) |
| 105. C23 | C22×#87604 | semidirect |
| 117. C22 | C2×C22⋊#87604 | direct (N × H) |
| 119. C22 | C23×#87604 | semidirect |
| 125. C2 | C22×C22⋊#87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#87604 | 2 |
| C22×C22⋊#87604 | 2 |
| C25×D97 | 2 |
| C23×C22⋊C4 | 97 |