Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic181 | C2 | semidirect |
| 3. #26041612 | C2 | semidirect |
| 5. #26041584 | C2 | semidirect |
| 6. #26041503 | C2 | semidirect |
| 8. #26041386 | C2 | semidirect |
| 9. #26041382 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #451×C181 | C2 | semidirect |
| 131. C181 | #3117 | semidirect |
| 139. #451 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041815 | 2 |
| C2×Q8×Dic181 | 2 |
| #26041612 | 2 |
| #26041598 | 2 |
| #26041584 | 2 |
| #26041503 | 2 |
| #26041418 | 2 |
| #26041386 | 2 |
| #26041382 | 2 |
| #26041333 | 2 |
| #451×C181 | 2 |
| #3117 | 181 |