Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 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×Q8×D97 | C2 | semidirect |
| 2. Q8×D388 | C2 | direct (N × H) |
| 3. C2×#15690810 | C2 | semidirect |
| 4. C2×#15690790 | C2 | semidirect |
| 6. C2×C4×Q8×C97 | C2 | semidirect |
| 9. C2×Q8×D97 | C22 | semidirect |
| 12. #15690810 | C22 | semidirect |
| 13. #15690790 | C22 | semidirect |
| 19. C4×Q8×C97 | C22 | semidirect |
| 26. C2×D388 | Q8 | direct (N × H) |
| 34. C2×Q8×C97 | D4 | semidirect |
| 44. C22×D97 | C2×Q8 | semidirect |
| 46. Q8×C97 | C2×D4 | semidirect |
| 49. C2×C4×C97 | C2×Q8 | semidirect |
| 55. D388 | C2×Q8 | direct (N × H) |
| 65. C2×D97 | C22×Q8 | semidirect |
| 68. C4×C97 | C22×Q8 | semidirect |
| 70. C2×C97 | D4×Q8 | semidirect |
| 76. C97 | C2×D4×Q8 | semidirect |
| 81. C2×C4×Q8 | D97 | semidirect |
| 91. C4×Q8 | C2×D97 | semidirect |
| 102. C2×Q8 | D388 | direct (N × H) |
| 123. Q8 | C2×D388 | direct (N × H) |
| 130. C2×C4 | Q8×D97 | semidirect |
| 145. C4 | C2×Q8×D97 | semidirect |
| 147. C2 | Q8×D388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D97 | 2 |
| Q8×D388 | 2 |
| C2×#15690810 | 2 |
| C2×#15690790 | 2 |
| C2×C4×D388 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×D4×Q8 | 97 |