Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
854 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 152 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. #22625025 | C2 | semidirect |
| 6. #17989566 | C4 | semidirect |
| 10. C2×#14556550 | C4 | semidirect |
| 11. #17988493 | C4 | semidirect |
| 15. C22×C42×C73 | C4 | semidirect |
| 22. #14556650 | C2×C4 | semidirect |
| 173. C73 | #12581 | semidirect |
| 177. C22×C42 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989566 | 2 |
| #22625025 | 2 |
| #22612421 | 2 |
| #12581 | 73 |