Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19153799 | C2 | semidirect |
| 3. #26041181 | C2 | semidirect |
| 4. #26041177 | C2 | semidirect |
| 5. #26041170 | C2 | semidirect |
| 6. #26041158 | C2 | semidirect |
| 7. #26041139 | C2 | semidirect |
| 8. C22×C42×C181 | C2 | semidirect |
| 50. C22×C4×C181 | D4 | semidirect |
| 107. C4×C181 | #123 | semidirect |
| 117. C181 | #2854 | semidirect |
| 121. C22×C42 | D181 | semidirect |
| 161. C22×C4 | D724 | semidirect |
| 227. C4 | #19153799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153799 | 2 |
| C2×#19153790 | 2 |
| #26041181 | 2 |
| #26041177 | 2 |
| #26041170 | 2 |
| #26041158 | 2 |
| #26041139 | 2 |
| C22×C42×C181 | 2 |
| #2854 | 181 |