Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 3. #26041650 | C2 | semidirect |
| 4. #26041628 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 7. #26041481 | C2 | semidirect |
| 8. #26041419 | C2 | semidirect |
| 9. #26041416 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #461×C181 | C2 | semidirect |
| 107. C4×D181 | SD16 | semidirect |
| 148. C181 | #3206 | semidirect |
| 157. #461 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041826 | 2 |
| C4⋊Q8×D181 | 2 |
| #26041650 | 2 |
| #26041628 | 2 |
| #26041485 | 2 |
| #26041484 | 2 |
| #26041481 | 2 |
| #26041419 | 2 |
| #26041416 | 2 |
| #26041331 | 2 |
| #461×C181 | 2 |
| #3206 | 181 |