Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15690835 | C2 | semidirect |
| 2. C2×#15690816 | C2 | semidirect |
| 3. #20261313 | C2 | semidirect |
| 4. #20261304 | C2 | semidirect |
| 5. #20260987 | C2 | semidirect |
| 6. #20260984 | C2 | semidirect |
| 7. #20260970 | C2 | semidirect |
| 8. #20260967 | C2 | semidirect |
| 9. #20260778 | C2 | semidirect |
| 10. C2×#15690732 | C2 | semidirect |
| 11. #416×C97 | C2 | semidirect |
| 19. C2×#13095494 | C22 | semidirect |
| 20. C2×C8×D97 | C22 | semidirect |
| 24. #15690786 | C22 | semidirect |
| 29. #15690781 | C22 | semidirect |
| 32. #15690743 | C22 | semidirect |
| 33. #15690741 | C22 | semidirect |
| 39. #103×C97 | C22 | semidirect |
| 40. #103×C97 | C22 | semidirect |
| 41. #102×C97 | C22 | semidirect |
| 42. #102×C97 | C22 | semidirect |
| 60. #13095495 | D4 | semidirect |
| 152. C97 | #3062 | semidirect |
| 162. #416 | D97 | semidirect |
| 189. #103 | C2×D97 | semidirect |
| 190. #103 | C2×D97 | semidirect |
| 193. #102 | C2×D97 | semidirect |
| 194. #102 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C2×#15690816 | 2 |
| #20261313 | 2 |
| #20261304 | 2 |
| #20260987 | 2 |
| #20260984 | 2 |
| #20260970 | 2 |
| #20260967 | 2 |
| #20260778 | 2 |
| C2×#15690732 | 2 |
| #416×C97 | 2 |
| #3062 | 97 |