Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041829 | C2 | semidirect |
| 2. C4×#15668449 | C2 | semidirect |
| 3. #26041604 | C2 | semidirect |
| 4. #26041565 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041480 | C2 | semidirect |
| 7. #26041475 | C2 | semidirect |
| 8. #26041426 | C2 | semidirect |
| 9. #26041392 | C2 | semidirect |
| 10. #26041381 | C2 | semidirect |
| 11. #432×C181 | C2 | semidirect |
| 87. Dic362 | #41 | semidirect |
| 93. D724 | #41 | semidirect |
| 144. C181 | #3115 | semidirect |
| 156. #432 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| C4×#15668449 | 2 |
| #26041604 | 2 |
| #26041565 | 2 |
| #26041560 | 2 |
| #26041480 | 2 |
| #26041475 | 2 |
| #26041426 | 2 |
| #26041392 | 2 |
| #26041381 | 2 |
| #432×C181 | 2 |
| #3115 | 181 |