Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. D4×Dic362 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 6. #26041558 | C2 | semidirect |
| 7. #26041474 | C2 | semidirect |
| 8. #26041472 | C2 | semidirect |
| 9. C8×Dic362 | C2 | semidirect |
| 10. #26041359 | C2 | semidirect |
| 11. C4×D8×C181 | C2 | semidirect |
| 78. Dic362 | D8 | semidirect |
| 96. D4×C181 | #41 | semidirect |
| 131. C181 | #3358 | semidirect |
| 143. C4×D8 | D181 | semidirect |
| 222. D4 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041950 | 2 |
| D4×Dic362 | 2 |
| #26041626 | 2 |
| #26041624 | 2 |
| #26041559 | 2 |
| #26041558 | 2 |
| #26041474 | 2 |
| #26041472 | 2 |
| C8×Dic362 | 2 |
| #26041359 | 2 |
| C4×D8×C181 | 2 |
| #3358 | 181 |