Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22612848 | C2 | semidirect |
| 5. #22608325 | C2 | semidirect |
| 6. #22607832 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 13. #17988798 | C4 | semidirect |
| 14. #17988788 | C4 | semidirect |
| 208. #1286 | D73 | semidirect |
| 209. C73 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619405 | 2 |
| #22612848 | 2 |
| #22608490 | 2 |
| #22608427 | 2 |
| #22608325 | 2 |
| #22607832 | 2 |
| C73×#1286 | 2 |
| #9180 | 73 |