Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26041170 | C2 | semidirect |
| 4. #26041162 | C2 | semidirect |
| 5. #26041157 | C2 | semidirect |
| 6. #26041155 | C2 | semidirect |
| 7. #26041142 | C2 | semidirect |
| 8. C4×#15668426 | C2 | semidirect |
| 9. C4×C22⋊C4×C181 | C2 | semidirect |
| 13. #19153790 | C4 | semidirect |
| 38. C2×C22⋊D181 | C2×C4 | semidirect |
| 45. C4⋊Dic181 | C2×C4 | semidirect |
| 52. #15668426 | C2×C4 | semidirect |
| 57. C22×C4×C181 | C2×C4 | semidirect |
| 134. C181 | #2333 | semidirect |
| 144. C4×C22⋊C4 | D181 | semidirect |
| 183. 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 |
| #26041170 | 2 |
| #26041162 | 2 |
| #26041157 | 2 |
| #26041155 | 2 |
| #26041142 | 2 |
| C4×#15668426 | 2 |
| C4×C22⋊C4×C181 | 2 |
| #2333 | 181 |