Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D181 | C2 | semidirect |
| 3. #26041673 | C2 | semidirect |
| 4. #26041671 | C2 | semidirect |
| 5. #26041649 | C2 | semidirect |
| 6. #26041488 | C2 | semidirect |
| 7. #26041483 | C2 | semidirect |
| 8. #26041436 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #491×C181 | C2 | semidirect |
| 135. C181 | #3218 | semidirect |
| 142. #491 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D181 | 2 |
| #26041814 | 2 |
| #26041673 | 2 |
| #26041671 | 2 |
| #26041649 | 2 |
| #26041488 | 2 |
| #26041483 | 2 |
| #26041436 | 2 |
| #26041419 | 2 |
| #26041334 | 2 |
| #491×C181 | 2 |
| #3218 | 181 |