Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. #20261746 | C2 | semidirect |
| 3. #20261745 | C2 | semidirect |
| 4. C2×#15690878 | C2 | semidirect |
| 15. #15690818 | C4 | semidirect |
| 16. #15690817 | C4 | semidirect |
| 17. #15690816 | C4 | semidirect |
| 20. #131×C97 | C4 | semidirect |
| 33. #13095495 | C2×C4 | semidirect |
| 34. #13095494 | C2×C4 | semidirect |
| 35. C2×#11715895 | C2×C4 | semidirect |
| 36. C8×D97 | C2×C4 | semidirect |
| 37. C8×D97 | C2×C4 | semidirect |
| 41. M16×C97 | C2×C4 | semidirect |
| 42. C2×C8×C97 | C2×C4 | semidirect |
| 77. C97 | #2912 | semidirect |
| 87. #131 | #87604 | semidirect |
| 108. M16 | C2×#87604 | semidirect |
| 114. C2×C8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261804 | 2 |
| #20261746 | 2 |
| #20261745 | 2 |
| C2×#15690878 | 2 |
| #131×D97 | 2 |
| #2912 | 97 |