Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153849 | C2 | semidirect |
| 3. C22×#15668439 | C2 | semidirect |
| 4. #26041855 | C2 | semidirect |
| 5. #26041444 | C2 | semidirect |
| 6. #26041436 | C2 | semidirect |
| 7. #26041273 | C2 | semidirect |
| 8. #26041247 | C2 | semidirect |
| 9. #419×C181 | C2 | semidirect |
| 140. C181 | #3011 | semidirect |
| 148. #419 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153864 | 2 |
| C2×#19153849 | 2 |
| C22×#15668439 | 2 |
| #26041855 | 2 |
| #26041444 | 2 |
| #26041436 | 2 |
| #26041273 | 2 |
| #26041247 | 2 |
| #419×C181 | 2 |
| #3011 | 181 |