Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 74 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. #26042157 | C2 | semidirect |
| 8. C23×Dic181 | C4 | semidirect |
| 11. C2×#15668426 | C4 | semidirect |
| 13. C23×C4×C181 | C4 | semidirect |
| 100. C181 | #1819 | semidirect |
| 107. C23×C4 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042220 | 2 |
| #26042157 | 2 |
| C22×#15668426 | 2 |
| #1819 | 181 |