Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1088 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 261 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×#19153772 | C2 | semidirect |
| 3. #26041140 | C2 | semidirect |
| 4. #26041137 | C2 | semidirect |
| 6. C22⋊C4×Dic181 | C2 | semidirect |
| 9. C23×Dic181 | C4 | semidirect |
| 15. C2×#15668428 | C22 | semidirect |
| 18. C2×C4×Dic181 | C22 | semidirect |
| 19. #19153723 | C22 | semidirect |
| 54. C2×Dic181 | C22⋊C4 | semidirect |
| 80. C22×C181 | #117 | semidirect |
| 94. C181 | #2280 | semidirect |
| 175. C22 | #19153772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic181 | 2 |
| C2×#19153772 | 2 |
| #26041140 | 2 |
| #26041137 | 2 |
| #26041135 | 2 |
| C22⋊C4×Dic181 | 2 |
| #379×C181 | 2 |
| #2280 | 181 |