Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #26041623 | C2 | semidirect |
| 4. #26041622 | C2 | semidirect |
| 5. #26041616 | C2 | semidirect |
| 6. #26041611 | C2 | semidirect |
| 7. #26041322 | C2 | semidirect |
| 8. #26041287 | C2 | semidirect |
| 9. C2×#19153741 | C2 | semidirect |
| 11. #427×C181 | C2 | semidirect |
| 126. C181 | #3097 | semidirect |
| 135. #427 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041855 | 2 |
| #26041759 | 2 |
| #26041623 | 2 |
| #26041622 | 2 |
| #26041616 | 2 |
| #26041611 | 2 |
| #26041322 | 2 |
| #26041287 | 2 |
| C2×#19153741 | 2 |
| #26041245 | 2 |
| #427×C181 | 2 |
| #3097 | 181 |