Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26041142 | C2 | semidirect |
| 3. #26041014 | C2 | semidirect |
| 4. #407×C181 | C2 | semidirect |
| 5. C22×D724 | C4 | semidirect |
| 9. #19153790 | C4 | semidirect |
| 11. C2×C4⋊Dic181 | C4 | semidirect |
| 15. #19153723 | C22 | semidirect |
| 19. C22⋊C8×C181 | C22 | semidirect |
| 102. C181 | #1510 | semidirect |
| 105. #407 | D181 | semidirect |
| 120. C22⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153790 | 2 |
| #26041142 | 2 |
| #26041014 | 2 |
| #407×C181 | 2 |
| #1510 | 181 |