Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22608722 | C2 | semidirect |
| 5. #22607820 | C2 | semidirect |
| 6. #22607768 | C2 | semidirect |
| 7. C73×#1837 | C2 | semidirect |
| 168. #1837 | D73 | semidirect |
| 174. C73 | #8901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619061 | 2 |
| #22608722 | 2 |
| #22608368 | 2 |
| #22608314 | 2 |
| #22607820 | 2 |
| #22607768 | 2 |
| C73×#1837 | 2 |
| #8901 | 73 |