Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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. #26042033 | C2 | semidirect |
| 3. #26041643 | C2 | semidirect |
| 4. #26041021 | C2 | semidirect |
| 5. #26041020 | C2 | semidirect |
| 6. #26041018 | C2 | semidirect |
| 7. #490×C181 | C2 | semidirect |
| 97. C181 | #1657 | semidirect |
| 102. #490 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042033 | 2 |
| #26041666 | 2 |
| #26041643 | 2 |
| #26041021 | 2 |
| #26041020 | 2 |
| #26041018 | 2 |
| #490×C181 | 2 |
| #1657 | 181 |