Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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. #26042125 | C2 | semidirect |
| 42. C2×Dic181 | M16 | semidirect |
| 75. C181 | #1463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042249 | 2 |
| #26042125 | 2 |
| C22×#15668428 | 2 |
| #1463 | 181 |