Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
200 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 13. #19153749 | C4 | semidirect |
| 14. #19153747 | C4 | semidirect |
| 75. C181 | #1946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153751 | 2 |
| #26041315 | 2 |
| #26041307 | 2 |
| #26041306 | 2 |
| C2×#19153727 | 2 |
| #26041039 | 2 |
| #339×C181 | 2 |
| #1946 | 181 |