Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26041295 | C2 | semidirect |
| 3. #26041275 | C2 | semidirect |
| 4. #26041273 | C2 | semidirect |
| 5. #26041252 | C2 | semidirect |
| 6. #26041247 | C2 | semidirect |
| 7. #421×C181 | C2 | semidirect |
| 10. #19153863 | C4 | semidirect |
| 12. #19153862 | C4 | semidirect |
| 20. C22×#13089678 | C22 | semidirect |
| 21. #19153775 | C22 | semidirect |
| 30. C2×M16×C181 | C22 | semidirect |
| 31. #117×C181 | C22 | semidirect |
| 166. C181 | #1794 | semidirect |
| 170. #421 | D181 | semidirect |
| 188. C2×M16 | C2×D181 | semidirect |
| 191. #117 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042115 | 2 |
| #26041295 | 2 |
| #26041275 | 2 |
| #26041273 | 2 |
| #26041252 | 2 |
| #26041247 | 2 |
| #421×C181 | 2 |
| #1794 | 181 |