Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#15690733 | C2 | semidirect |
| 5. C2×#15690728 | C2 | semidirect |
| 6. #20260499 | C2 | semidirect |
| 7. #343×C97 | C2 | semidirect |
| 11. #15690843 | C4 | semidirect |
| 117. C97 | #1908 | semidirect |
| 123. #343 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| C2×#15690818 | 2 |
| #20260734 | 2 |
| C2×#15690733 | 2 |
| C2×#15690728 | 2 |
| #20260499 | 2 |
| #343×C97 | 2 |
| #1908 | 97 |