Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 120 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. #22626288 | C2 | semidirect |
| 2. #22624868 | C2 | semidirect |
| 56. C2×C4×D73 | C16 | semidirect |
| 144. C73 | #11459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626288 | 2 |
| #22624868 | 2 |
| #22624852 | 2 |
| C2×#17988638 | 2 |
| #11459 | 73 |