Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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. C8×Dic362 | C2 | semidirect |
| 3. #26041403 | C2 | semidirect |
| 24. C2×Dic362 | C8 | semidirect |
| 78. C181 | #2982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic362 | 2 |
| C8×Dic362 | 2 |
| #26041403 | 2 |
| #26041332 | 2 |
| #26041329 | 2 |
| #431×C181 | 2 |
| #2982 | 181 |