Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×D776 | C2 | semidirect |
| 2. C2×#15690751 | C2 | direct (N × H) |
| 3. C22×#13095486 | C2 | semidirect |
| 4. C22×D8×C97 | C2 | semidirect |
| 7. C2×D776 | C22 | semidirect |
| 8. #15690751 | C22 | direct (N × H) |
| 9. C2×#13095486 | C22 | semidirect |
| 12. C2×D8×C97 | C22 | semidirect |
| 18. D776 | C23 | semidirect |
| 19. #13095486 | C23 | semidirect |
| 25. D8×C97 | C23 | semidirect |
| 43. C22×C97 | D16 | semidirect |
| 50. C2×C97 | C2×D16 | semidirect |
| 54. C97 | C22×D16 | semidirect |
| 56. C22×D8 | D97 | semidirect |
| 64. C2×D8 | C2×D97 | semidirect |
| 78. D8 | C22×D97 | semidirect |
| 99. C22 | #15690751 | direct (N × H) |
| 105. C2 | C2×#15690751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×#15690751 | 2 |
| C22×#13095486 | 2 |
| C22×D8×C97 | 2 |
| C22×D16 | 97 |