Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041830 | C2 | semidirect |
| 2. C4×#15668450 | C2 | semidirect |
| 3. #26041606 | C2 | semidirect |
| 4. #26041566 | C2 | semidirect |
| 5. #26041479 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041427 | C2 | semidirect |
| 8. #26041364 | C2 | semidirect |
| 9. #26041361 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #477×C181 | C2 | semidirect |
| 93. D724 | #41 | semidirect |
| 109. Q8×C181 | #41 | semidirect |
| 144. C181 | #3106 | semidirect |
| 149. #477 | D181 | semidirect |
| 233. Q8 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041830 | 2 |
| C4×#15668450 | 2 |
| #26041606 | 2 |
| #26041566 | 2 |
| #26041479 | 2 |
| #26041475 | 2 |
| #26041427 | 2 |
| #26041364 | 2 |
| #26041361 | 2 |
| #26041331 | 2 |
| #477×C181 | 2 |
| #3106 | 181 |