Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26042221 | C2 | semidirect |
| 3. #26042157 | C2 | semidirect |
| 10. C22×C4×D181 | C4 | semidirect |
| 14. C2×#15668426 | C4 | semidirect |
| 16. C2×C4×Dic181 | C4 | semidirect |
| 17. C2×C4⋊C4×C181 | C4 | semidirect |
| 53. C22×D181 | C4⋊C4 | semidirect |
| 76. C2×C4×C181 | C4⋊C4 | semidirect |
| 100. Dic181 | #99 | semidirect |
| 109. C181 | #1799 | semidirect |
| 121. C2×C4⋊C4 | #10624382 | semidirect |
| 186. C2×C4 | C4⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153875 | 2 |
| #26042221 | 2 |
| #26042157 | 2 |
| C2×#19153778 | 2 |
| #1799 | 181 |