Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #125×D181 | C2 | semidirect |
| 3. #26041646 | C2 | semidirect |
| 4. #26041642 | C2 | semidirect |
| 5. #26041636 | C2 | semidirect |
| 6. #26041634 | C2 | semidirect |
| 7. #26041633 | C2 | semidirect |
| 8. #26041279 | C2 | semidirect |
| 9. #26041277 | C2 | semidirect |
| 10. C4×#15668432 | C2 | semidirect |
| 11. #488×C181 | C2 | semidirect |
| 114. C181 | #3142 | semidirect |
| 123. #488 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041828 | 2 |
| #125×D181 | 2 |
| #26041646 | 2 |
| #26041642 | 2 |
| #26041636 | 2 |
| #26041634 | 2 |
| #26041633 | 2 |
| #26041279 | 2 |
| #26041277 | 2 |
| C4×#15668432 | 2 |
| #488×C181 | 2 |
| #3142 | 181 |