Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4⋊Q8×D181 | C2 | semidirect |
| 3. #26041676 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041599 | C2 | semidirect |
| 6. #26041596 | C2 | semidirect |
| 7. #26041570 | C2 | semidirect |
| 8. #26041569 | C2 | semidirect |
| 9. #26041566 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 141. C181 | #3227 | semidirect |
| 152. #476 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041826 | 2 |
| C4⋊Q8×D181 | 2 |
| #26041676 | 2 |
| #26041624 | 2 |
| #26041599 | 2 |
| #26041596 | 2 |
| #26041570 | 2 |
| #26041569 | 2 |
| #26041566 | 2 |
| #26041331 | 2 |
| #476×C181 | 2 |
| #3227 | 181 |