Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26041400 | C2 | semidirect |
| 3. #26041391 | C2 | semidirect |
| 4. #26041103 | C2 | semidirect |
| 5. #26041090 | C2 | semidirect |
| 6. #26041056 | C2 | semidirect |
| 7. #361×C181 | C2 | semidirect |
| 11. #19153760 | C4 | semidirect |
| 12. #19153757 | C4 | semidirect |
| 23. Dic724 | C2×C4 | semidirect |
| 25. D1448 | C2×C4 | semidirect |
| 32. #15668424 | C2×C4 | semidirect |
| 68. C181 | AGL(1,ℤ/16) | semidirect |
| 74. #361 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041715 | 2 |
| #26041400 | 2 |
| #26041391 | 2 |
| #26041103 | 2 |
| #26041090 | 2 |
| #26041056 | 2 |
| #361×C181 | 2 |
| AGL(1,ℤ/16) | 181 |