Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26041396 | C2 | semidirect |
| 3. #26041395 | C2 | semidirect |
| 4. #26041108 | C2 | semidirect |
| 5. #26041087 | C2 | semidirect |
| 6. C16×Dic181 | C2 | semidirect |
| 7. #359×C181 | C2 | semidirect |
| 11. #19153762 | C4 | semidirect |
| 12. #19153760 | C4 | semidirect |
| 13. #19153759 | C4 | semidirect |
| 14. #19153757 | C4 | semidirect |
| 71. C181 | #2178 | semidirect |
| 78. #359 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041709 | 2 |
| #26041396 | 2 |
| #26041395 | 2 |
| #26041108 | 2 |
| #26041087 | 2 |
| C16×Dic181 | 2 |
| #359×C181 | 2 |
| #2178 | 181 |