Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26041835 | C2 | semidirect |
| 3. #26041685 | C2 | semidirect |
| 4. #26041645 | C2 | semidirect |
| 5. #26041644 | C2 | semidirect |
| 6. #26041606 | C2 | semidirect |
| 7. #26041605 | C2 | semidirect |
| 8. #26041568 | C2 | semidirect |
| 9. #26041558 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #501×C181 | C2 | semidirect |
| 128. C181 | #3235 | semidirect |
| 133. #501 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041835 | 2 |
| #26041830 | 2 |
| #26041685 | 2 |
| #26041645 | 2 |
| #26041644 | 2 |
| #26041606 | 2 |
| #26041605 | 2 |
| #26041568 | 2 |
| #26041558 | 2 |
| #26041334 | 2 |
| #501×C181 | 2 |
| #3235 | 181 |