Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
| 4. #26041490 | C2 | semidirect |
| 5. #26041488 | C2 | semidirect |
| 6. #26041486 | C2 | semidirect |
| 7. #26041484 | C2 | semidirect |
| 8. #26041482 | C2 | semidirect |
| 9. #26041301 | C2 | semidirect |
| 10. #26041286 | C2 | semidirect |
| 11. #461×C181 | C2 | semidirect |
| 131. C4×C181 | #137 | semidirect |
| 139. Dic181 | #137 | semidirect |
| 145. C181 | #3039 | semidirect |
| 155. #461 | D181 | semidirect |
| 283. C4 | #19153845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153845 | 2 |
| C4⋊Q8×D181 | 2 |
| C4×#15668448 | 2 |
| #26041490 | 2 |
| #26041488 | 2 |
| #26041486 | 2 |
| #26041484 | 2 |
| #26041482 | 2 |
| #26041301 | 2 |
| #26041286 | 2 |
| #461×C181 | 2 |
| #3039 | 181 |