Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22611469 | C2 | semidirect |
| 3. #22611468 | C2 | semidirect |
| 5. #22607756 | C2 | semidirect |
| 7. C73×#1272 | C2 | semidirect |
| 200. #1272 | D73 | semidirect |
| 202. C73 | #7833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617875 | 2 |
| #22611469 | 2 |
| #22611468 | 2 |
| #22611463 | 2 |
| #22607756 | 2 |
| #22607751 | 2 |
| C73×#1272 | 2 |
| #7833 | 73 |