Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. C2×#19153814 | C2 | semidirect |
| 3. #26041650 | C2 | semidirect |
| 4. #26041628 | C2 | semidirect |
| 5. #26041483 | C2 | semidirect |
| 6. #26041482 | C2 | semidirect |
| 7. #26041420 | C2 | semidirect |
| 8. #26041418 | C2 | semidirect |
| 9. #26041417 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #448×C181 | C2 | semidirect |
| 99. C2×Dic181 | SD16 | semidirect |
| 146. C181 | #3206 | semidirect |
| 157. #448 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×#19153814 | 2 |
| #26041650 | 2 |
| #26041628 | 2 |
| #26041483 | 2 |
| #26041482 | 2 |
| #26041420 | 2 |
| #26041418 | 2 |
| #26041417 | 2 |
| #26041329 | 2 |
| #448×C181 | 2 |
| #3206 | 181 |