Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26042045 | C2 | semidirect |
| 3. #26041273 | C2 | semidirect |
| 4. #26041246 | C2 | semidirect |
| 5. #26041049 | C2 | semidirect |
| 6. #26041043 | C2 | semidirect |
| 7. #421×C181 | C2 | semidirect |
| 9. #19153847 | C4 | semidirect |
| 11. #19153842 | C4 | semidirect |
| 118. C181 | #1881 | semidirect |
| 122. #421 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| #26042045 | 2 |
| #26041273 | 2 |
| #26041246 | 2 |
| #26041049 | 2 |
| #26041043 | 2 |
| #421×C181 | 2 |
| #1881 | 181 |