Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041824 | C2 | semidirect |
| 2. #26041558 | C2 | semidirect |
| 3. #26041557 | C2 | semidirect |
| 4. #26041515 | C2 | semidirect |
| 5. #26041513 | C2 | semidirect |
| 6. #26041473 | C2 | semidirect |
| 7. #26041472 | C2 | semidirect |
| 8. C2×#19153745 | C2 | semidirect |
| 9. #466×C181 | C2 | semidirect |
| 75. C2×Dic181 | D8 | semidirect |
| 115. C181 | #3245 | semidirect |
| 122. #466 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| #26041558 | 2 |
| #26041557 | 2 |
| #26041515 | 2 |
| #26041513 | 2 |
| #26041473 | 2 |
| #26041472 | 2 |
| C2×#19153745 | 2 |
| #466×C181 | 2 |
| #3245 | 181 |