Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
936 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 285 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. C2×#19153775 | C2 | semidirect |
| 3. #26041185 | C2 | semidirect |
| 4. #26041181 | C2 | semidirect |
| 5. #26041158 | C2 | semidirect |
| 6. C4×#15668426 | C2 | semidirect |
| 7. C22×C42×C181 | C2 | semidirect |
| 10. C2×#15668449 | C4 | semidirect |
| 30. C2×Dic362 | C2×C4 | semidirect |
| 33. C2×D724 | C2×C4 | semidirect |
| 41. C2×C4×D181 | C2×C4 | semidirect |
| 78. C2×C4×C181 | C22⋊C4 | semidirect |
| 85. C2×C4×C181 | #41 | semidirect |
| 109. C181 | #2297 | semidirect |
| 113. C22×C42 | D181 | semidirect |
| 188. C2×C4 | #15668426 | semidirect |
| 195. C2×C4 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668449 | 2 |
| C2×#19153775 | 2 |
| #26041185 | 2 |
| #26041181 | 2 |
| #26041158 | 2 |
| C4×#15668426 | 2 |
| C22×C42×C181 | 2 |
| #2297 | 181 |