Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #26041829 | C2 | semidirect |
| 2. #26041655 | C2 | semidirect |
| 3. #26041653 | C2 | semidirect |
| 4. #26041629 | C2 | semidirect |
| 5. #26041625 | C2 | semidirect |
| 6. #26041491 | C2 | semidirect |
| 7. #26041424 | C2 | semidirect |
| 8. #26041332 | C2 | semidirect |
| 9. #532×C181 | C2 | semidirect |
| 120. C181 | #3207 | semidirect |
| 123. #532 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041655 | 2 |
| #26041653 | 2 |
| #26041629 | 2 |
| #26041625 | 2 |
| #26041491 | 2 |
| #26041424 | 2 |
| #26041332 | 2 |
| #532×C181 | 2 |
| #3207 | 181 |