Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
200 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 94 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. #20261597 | C2 | semidirect |
| 3. #20261596 | C2 | semidirect |
| 23. C8×D97 | C8 | semidirect |
| 43. C8×C97 | C2×C8 | semidirect |
| 45. #11715895 | C2×C8 | semidirect |
| 60. D97 | #334 | semidirect |
| 62. C97 | C2×#334 | semidirect |
| 107. C8 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261736 | 2 |
| #20261597 | 2 |
| #20261596 | 2 |
| C4×C8×D97 | 2 |
| C2×#334 | 97 |