Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26041566 | C2 | semidirect |
| 3. #26041028 | C2 | semidirect |
| 4. #26041008 | C2 | semidirect |
| 5. #494×C181 | C2 | semidirect |
| 60. C181 | #1634 | semidirect |
| 63. #494 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041995 | 2 |
| #26041566 | 2 |
| #26041028 | 2 |
| #26041008 | 2 |
| #494×C181 | 2 |
| #1634 | 181 |