Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26041832 | C2 | semidirect |
| 3. #26041635 | C2 | semidirect |
| 4. #26041632 | C2 | semidirect |
| 5. #26041628 | C2 | semidirect |
| 6. #26041624 | C2 | semidirect |
| 7. #26041276 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 9. #26041273 | C2 | semidirect |
| 10. C2×C8×Dic181 | C2 | semidirect |
| 11. #416×C181 | C2 | semidirect |
| 125. C181 | #3131 | semidirect |
| 136. #416 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| #26041825 | 2 |
| #26041635 | 2 |
| #26041632 | 2 |
| #26041628 | 2 |
| #26041624 | 2 |
| #26041276 | 2 |
| #26041275 | 2 |
| #26041273 | 2 |
| C2×C8×Dic181 | 2 |
| #416×C181 | 2 |
| #3131 | 181 |