Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×Dic584 | C2 | semidirect |
| 4. C2×#17988390 | C2 | semidirect |
| 5. #22610790 | C2 | semidirect |
| 6. #22608008 | C2 | semidirect |
| 199. C73 | #13329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic584 | 2 |
| C22×#14556535 | 2 |
| C2×#17988970 | 2 |
| C2×#17988390 | 2 |
| #22610790 | 2 |
| #22608008 | 2 |
| C2×#357×C73 | 2 |
| #13329 | 73 |