Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26041826 | C2 | semidirect |
| 3. #26041570 | C2 | semidirect |
| 4. #26041569 | C2 | semidirect |
| 5. #26041567 | C2 | semidirect |
| 6. #26041531 | C2 | semidirect |
| 7. #26041529 | C2 | semidirect |
| 8. #26041472 | C2 | semidirect |
| 9. #26041471 | C2 | semidirect |
| 10. #26041301 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 150. C181 | #3253 | semidirect |
| 161. #459 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| #26041826 | 2 |
| #26041570 | 2 |
| #26041569 | 2 |
| #26041567 | 2 |
| #26041531 | 2 |
| #26041529 | 2 |
| #26041472 | 2 |
| #26041471 | 2 |
| #26041301 | 2 |
| #459×C181 | 2 |
| #3253 | 181 |