Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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. #26042278 | C2 | semidirect |
| 2. #26042272 | C2 | semidirect |
| 3. #26042265 | C2 | semidirect |
| 4. #26042258 | C2 | semidirect |
| 17. C2×#15668450 | C4 | semidirect |
| 21. C2×#15668449 | C4 | semidirect |
| 24. C2×Q8×D181 | C4 | semidirect |
| 26. C22×Q8×C181 | C4 | semidirect |
| 141. C181 | #1796 | semidirect |
| 160. C22×Q8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042278 | 2 |
| #26042272 | 2 |
| #26042265 | 2 |
| #26042258 | 2 |
| C2×#19153864 | 2 |
| #1796 | 181 |