Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26041827 | C2 | semidirect |
| 2. C4×#15668448 | C2 | semidirect |
| 3. #26041602 | C2 | semidirect |
| 4. #26041565 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 6. #26041476 | C2 | semidirect |
| 7. #26041421 | C2 | semidirect |
| 8. #26041391 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 86. Dic362 | #41 | semidirect |
| 110. D4×C181 | #41 | semidirect |
| 144. C181 | #3115 | semidirect |
| 152. #459 | D181 | semidirect |
| 241. D4 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| C4×#15668448 | 2 |
| #26041602 | 2 |
| #26041565 | 2 |
| #26041559 | 2 |
| #26041476 | 2 |
| #26041421 | 2 |
| #26041391 | 2 |
| #26041376 | 2 |
| #26041335 | 2 |
| #459×C181 | 2 |
| #3115 | 181 |