Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19153848 | C2 | semidirect |
| 2. C2×#19153845 | C2 | semidirect |
| 4. C4⋊Q8×D181 | C2 | semidirect |
| 5. #26041674 | C2 | semidirect |
| 6. #26041673 | C2 | semidirect |
| 7. #26041671 | C2 | semidirect |
| 8. #26041657 | C2 | semidirect |
| 9. #26041650 | C2 | semidirect |
| 10. #26041231 | C2 | semidirect |
| 11. #497×C181 | C2 | semidirect |
| 63. #15668432 | D4 | semidirect |
| 124. Dic181 | #137 | semidirect |
| 130. C181 | #3152 | semidirect |
| 139. #497 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153848 | 2 |
| C2×#19153845 | 2 |
| #26041828 | 2 |
| C4⋊Q8×D181 | 2 |
| #26041674 | 2 |
| #26041673 | 2 |
| #26041671 | 2 |
| #26041657 | 2 |
| #26041650 | 2 |
| #26041231 | 2 |
| #497×C181 | 2 |
| #3152 | 181 |