Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #26041850 | C2 | semidirect |
| 3. #26041621 | C2 | semidirect |
| 4. #26041604 | C2 | semidirect |
| 5. #26041525 | C2 | semidirect |
| 6. #26041508 | C2 | semidirect |
| 7. #26041432 | C2 | semidirect |
| 8. #26041420 | C2 | semidirect |
| 9. #408×C181 | C2 | semidirect |
| 10. C22×Dic362 | C22 | semidirect |
| 21. #19153795 | C22 | semidirect |
| 27. #19153775 | C22 | semidirect |
| 28. #19153750 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 31. #19153741 | C22 | semidirect |
| 35. C2×M16×C181 | C22 | semidirect |
| 36. C22×C8×C181 | C22 | semidirect |
| 38. C22⋊C8×C181 | C22 | semidirect |
| 137. C181 | #3200 | semidirect |
| 147. #408 | D181 | semidirect |
| 153. C2×M16 | C2×D181 | semidirect |
| 154. C22×C8 | C2×D181 | semidirect |
| 176. C22⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041850 | 2 |
| #26041843 | 2 |
| #26041621 | 2 |
| #26041604 | 2 |
| #26041525 | 2 |
| #26041508 | 2 |
| #26041432 | 2 |
| #26041420 | 2 |
| #408×C181 | 2 |
| #3200 | 181 |