Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 1. #26042002 | C2 | semidirect |
| 3. #26041677 | C2 | semidirect |
| 4. #26041618 | C2 | semidirect |
| 5. #26041602 | C2 | semidirect |
| 6. #26041574 | C2 | semidirect |
| 7. #26041559 | C2 | semidirect |
| 8. #26041505 | C2 | semidirect |
| 9. C8×D724 | C2 | semidirect |
| 10. #26041314 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 120. C181 | #3340 | semidirect |
| 130. C4×SD16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041994 | 2 |
| #26041677 | 2 |
| #26041618 | 2 |
| #26041602 | 2 |
| #26041574 | 2 |
| #26041559 | 2 |
| #26041505 | 2 |
| C8×D724 | 2 |
| #26041314 | 2 |
| C4×SD16×C181 | 2 |
| #3340 | 181 |