Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
598 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C22⋊#10624382 | C2 | semidirect |
| 2. C2×#19153875 | C2 | semidirect |
| 3. #26042220 | C2 | semidirect |
| 4. #26042157 | C2 | semidirect |
| 15. C22×D724 | C4 | semidirect |
| 17. C22×C22⋊D181 | C4 | semidirect |
| 22. C2×#15668426 | C4 | semidirect |
| 24. C2×C22⋊C4×C181 | C4 | semidirect |
| 36. C22⋊#10624382 | D4 | semidirect |
| 42. C23×D181 | C2×C4 | semidirect |
| 58. C22×Dic181 | C2×C4 | semidirect |
| 64. C22×C4×C181 | C2×C4 | semidirect |
| 65. C22×C4×C181 | C2×C4 | semidirect |
| 133. C22×C181 | #99 | semidirect |
| 158. C2×D181 | #99 | semidirect |
| 179. C181 | #1898 | semidirect |
| 203. C2×C22⋊C4 | #10624382 | semidirect |
| 233. C22×C4 | C2×#10624382 | semidirect |
| 234. C22×C4 | C2×#10624382 | semidirect |
| 339. C22 | #19153875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| C2×#19153875 | 2 |
| #26042220 | 2 |
| #26042157 | 2 |
| C2×#19153786 | 2 |
| #1898 | 181 |