Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26041179 | C2 | semidirect |
| 3. #26041171 | C2 | semidirect |
| 4. #26041162 | C2 | semidirect |
| 5. #26041157 | C2 | semidirect |
| 6. #26041155 | C2 | semidirect |
| 7. #26041153 | C2 | semidirect |
| 8. #26041139 | C2 | semidirect |
| 9. #381×C181 | C2 | semidirect |
| 13. #19153790 | C4 | semidirect |
| 37. C2×C22⋊D181 | C2×C4 | semidirect |
| 45. C4⋊Dic181 | C2×C4 | semidirect |
| 52. #15668426 | C2×C4 | semidirect |
| 56. C22×C4×C181 | C2×C4 | semidirect |
| 129. C181 | #2377 | semidirect |
| 138. #381 | D181 | semidirect |
| 176. C22×C4 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153790 | 2 |
| #26041179 | 2 |
| #26041171 | 2 |
| #26041162 | 2 |
| #26041157 | 2 |
| #26041155 | 2 |
| #26041153 | 2 |
| #26041139 | 2 |
| #381×C181 | 2 |
| #2377 | 181 |