Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19153835 | C2 | semidirect |
| 2. C2×Q16×D181 | C2 | semidirect |
| 3. #26041937 | C2 | semidirect |
| 4. #26041517 | C2 | semidirect |
| 5. #26041512 | C2 | semidirect |
| 6. #26041498 | C2 | semidirect |
| 7. #26041438 | C2 | semidirect |
| 8. #26041416 | C2 | semidirect |
| 9. C4×Dic724 | C2 | semidirect |
| 10. C8×D724 | C2 | semidirect |
| 11. #495×C181 | C2 | semidirect |
| 54. Dic724 | D4 | semidirect |
| 120. C2×D181 | #135 | semidirect |
| 136. C181 | #3285 | semidirect |
| 141. #495 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| C2×Q16×D181 | 2 |
| #26041937 | 2 |
| #26041517 | 2 |
| #26041512 | 2 |
| #26041498 | 2 |
| #26041438 | 2 |
| #26041416 | 2 |
| C4×Dic724 | 2 |
| C8×D724 | 2 |
| #495×C181 | 2 |
| #3285 | 181 |