Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26041814 | C2 | semidirect |
| 3. #26041673 | C2 | semidirect |
| 4. #26041666 | C2 | semidirect |
| 5. #26041649 | C2 | semidirect |
| 6. #26041500 | C2 | semidirect |
| 7. #26041493 | C2 | semidirect |
| 8. #26041442 | C2 | semidirect |
| 9. #26041425 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #490×C181 | C2 | semidirect |
| 140. C181 | #3219 | semidirect |
| 147. #490 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| #26041814 | 2 |
| #26041673 | 2 |
| #26041666 | 2 |
| #26041649 | 2 |
| #26041500 | 2 |
| #26041493 | 2 |
| #26041442 | 2 |
| #26041425 | 2 |
| #26041334 | 2 |
| #490×C181 | 2 |
| #3219 | 181 |