Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #26041910 | C2 | semidirect |
| 3. #26041646 | C2 | semidirect |
| 4. #26041637 | C2 | semidirect |
| 5. #26041632 | C2 | semidirect |
| 6. #26041628 | C2 | semidirect |
| 7. #26041289 | C2 | semidirect |
| 9. C2×#19153739 | C2 | semidirect |
| 10. #26041237 | C2 | semidirect |
| 127. C181 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041910 | 2 |
| #26041850 | 2 |
| #26041646 | 2 |
| #26041637 | 2 |
| #26041632 | 2 |
| #26041628 | 2 |
| #26041289 | 2 |
| #26041275 | 2 |
| C2×#19153739 | 2 |
| #26041237 | 2 |
| #417×C181 | 2 |
| #3137 | 181 |