Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19153807 | C2 | semidirect |
| 3. #26041646 | C2 | semidirect |
| 4. #26041642 | C2 | semidirect |
| 5. #26041635 | C2 | semidirect |
| 6. #26041632 | C2 | semidirect |
| 7. #26041281 | C2 | semidirect |
| 8. #26041280 | C2 | semidirect |
| 9. #26041278 | C2 | semidirect |
| 10. M16×Dic181 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 146. C181 | #3142 | semidirect |
| 157. #417 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041825 | 2 |
| C2×#19153807 | 2 |
| #26041646 | 2 |
| #26041642 | 2 |
| #26041635 | 2 |
| #26041632 | 2 |
| #26041281 | 2 |
| #26041280 | 2 |
| #26041278 | 2 |
| M16×Dic181 | 2 |
| #417×C181 | 2 |
| #3142 | 181 |