Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
276 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 11. #15690809 | C4 | semidirect |
| 31. C2×#11715895 | Q8 | semidirect |
| 44. C2×C8×C97 | Q8 | semidirect |
| 102. C97 | #1993 | semidirect |
| 139. C2×C8 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690809 | 2 |
| C2×#15690720 | 2 |
| #20260600 | 2 |
| #20260498 | 2 |
| #20260497 | 2 |
| #340×C97 | 2 |
| #1993 | 97 |