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. #26041830 | C2 | semidirect |
| 2. C4×#15668448 | C2 | semidirect |
| 3. #26041606 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 5. #26041480 | C2 | semidirect |
| 6. #26041474 | C2 | semidirect |
| 7. #26041425 | C2 | semidirect |
| 8. #26041388 | C2 | semidirect |
| 9. #26041378 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 86. Dic362 | #41 | semidirect |
| 109. D4×C181 | #41 | semidirect |
| 144. C181 | #3115 | semidirect |
| 150. #474 | D181 | semidirect |
| 241. D4 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041830 | 2 |
| C4×#15668448 | 2 |
| #26041606 | 2 |
| #26041561 | 2 |
| #26041480 | 2 |
| #26041474 | 2 |
| #26041425 | 2 |
| #26041388 | 2 |
| #26041378 | 2 |
| #26041335 | 2 |
| #474×C181 | 2 |
| #3115 | 181 |