Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1880 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 810 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. C2×#15690889 | C2 | direct (N × H) |
| 2. C22×C4⋊#87604 | C2 | semidirect |
| 4. C22×C4×#87604 | C2 | semidirect |
| 7. #15690889 | C22 | direct (N × H) |
| 8. C2×C4⋊#87604 | C22 | semidirect |
| 10. C2×C4×#87604 | C22 | semidirect |
| 12. C23×Dic97 | C4 | semidirect |
| 13. C22×C4×D97 | C4 | semidirect |
| 14. C22×C4×D97 | C4 | semidirect |
| 15. C22×C4×D97 | C4 | semidirect |
| 19. C23×C4×C97 | C4 | semidirect |
| 22. C4⋊#87604 | C23 | semidirect |
| 24. C4×#87604 | C23 | semidirect |
| 32. C22×Dic97 | C2×C4 | semidirect |
| 35. C2×C4×D97 | C2×C4 | semidirect |
| 36. C2×C4×D97 | C2×C4 | semidirect |
| 37. C2×C4×D97 | C2×C4 | semidirect |
| 44. C22×C4×C97 | C2×C4 | semidirect |
| 61. C2×C4×C97 | C22×C4 | semidirect |
| 64. C2×Dic97 | C22×C4 | semidirect |
| 67. C4×D97 | C22×C4 | semidirect |
| 68. C4×D97 | C22×C4 | semidirect |
| 72. C22×C97 | #117 | semidirect |
| 78. C2×D97 | #117 | semidirect |
| 89. C2×C97 | C2×#117 | semidirect |
| 92. D97 | C2×#117 | semidirect |
| 95. C97 | C22×#117 | semidirect |
| 110. C23×C4 | #87604 | semidirect |
| 136. C22×C4 | C2×#87604 | semidirect |
| 165. C2×C4 | C22×#87604 | semidirect |
| 175. C22 | #15690889 | direct (N × H) |
| 187. C2 | C2×#15690889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| C22×C4⋊#87604 | 2 |
| C22×C22⋊#87604 | 2 |
| C22×C4×#87604 | 2 |
| C23×C4×D97 | 2 |
| C22×#117 | 97 |