Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611586 | C2 | semidirect |
| 5. #22610453 | C2 | semidirect |
| 6. #22608052 | C2 | semidirect |
| 7. C73×#1858 | C2 | semidirect |
| 200. #1858 | D73 | semidirect |
| 202. C73 | #13437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620804 | 2 |
| #22611586 | 2 |
| #22611582 | 2 |
| #22610458 | 2 |
| #22610453 | 2 |
| #22608052 | 2 |
| C73×#1858 | 2 |
| #13437 | 73 |