Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #26041683 | C2 | semidirect |
| 4. #26041628 | C2 | semidirect |
| 7. #26041575 | C2 | semidirect |
| 8. #26041574 | C2 | semidirect |
| 9. #26041571 | C2 | semidirect |
| 11. #477×C181 | C2 | semidirect |
| 128. C181 | #3230 | semidirect |
| 139. #477 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041833 | 2 |
| C4⋊Q8×D181 | 2 |
| #26041683 | 2 |
| #26041628 | 2 |
| #26041616 | 2 |
| #26041613 | 2 |
| #26041575 | 2 |
| #26041574 | 2 |
| #26041571 | 2 |
| #26041331 | 2 |
| #477×C181 | 2 |
| #3230 | 181 |