Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#19153844 | C2 | semidirect |
| 2. #26041829 | C2 | semidirect |
| 3. C2×C4×D724 | C2 | semidirect |
| 4. #26041495 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041281 | C2 | semidirect |
| 8. #423×C181 | C2 | semidirect |
| 15. #19153816 | C22 | semidirect |
| 16. #19153813 | C22 | semidirect |
| 17. #19153804 | C22 | semidirect |
| 28. #19153741 | C22 | semidirect |
| 29. #19153738 | C22 | semidirect |
| 32. C4⋊C8×C181 | C22 | semidirect |
| 33. C4⋊C8×C181 | C22 | semidirect |
| 42. C2×D724 | D4 | semidirect |
| 118. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 129. C181 | #3036 | semidirect |
| 137. #423 | D181 | semidirect |
| 160. C4⋊C8 | C2×D181 | semidirect |
| 161. C4⋊C8 | C2×D181 | semidirect |
| 250. C4 | #19153844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| #26041829 | 2 |
| C2×C4×D724 | 2 |
| #26041495 | 2 |
| #26041485 | 2 |
| #26041475 | 2 |
| #26041281 | 2 |
| #423×C181 | 2 |
| #3036 | 181 |