Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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. #26042157 | C2 | semidirect |
| 2. #26042123 | C2 | semidirect |
| 7. C22×D724 | C4 | semidirect |
| 10. #95×C181 | C4 | semidirect |
| 88. C181 | #1343 | semidirect |
| 99. #95 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042157 | 2 |
| #26042123 | 2 |
| #26041189 | 2 |
| #1343 | 181 |