Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041950 | C2 | semidirect |
| 2. #26041656 | C2 | semidirect |
| 3. #26041654 | C2 | semidirect |
| 4. #26041474 | C2 | semidirect |
| 5. #26041473 | C2 | semidirect |
| 6. C8×Dic362 | C2 | semidirect |
| 7. #26041361 | C2 | semidirect |
| 8. C4×D8×C181 | C2 | semidirect |
| 53. Dic362 | D8 | semidirect |
| 73. C8×C181 | #41 | semidirect |
| 93. C181 | #3391 | semidirect |
| 102. C4×D8 | D181 | semidirect |
| 167. C8 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041950 | 2 |
| #26041656 | 2 |
| #26041654 | 2 |
| #26041474 | 2 |
| #26041473 | 2 |
| C8×Dic362 | 2 |
| #26041361 | 2 |
| C4×D8×C181 | 2 |
| #3391 | 181 |