Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
710 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 136 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. #22625657 | C2 | semidirect |
| 2. C4×C22⋊#10596833 | C2 | semidirect |
| 4. #22624769 | C2 | semidirect |
| 12. #17989430 | C4 | semidirect |
| 232. C73 | #8155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625657 | 2 |
| C4×C22⋊#10596833 | 2 |
| C2×#17989430 | 2 |
| #22624769 | 2 |
| C2×#17988475 | 2 |
| #8155 | 73 |