Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22612898 | C2 | semidirect |
| 5. #22608325 | C2 | semidirect |
| 6. #22607832 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 12. #17988798 | C4 | semidirect |
| 13. #17988788 | C4 | semidirect |
| 204. #1286 | D73 | semidirect |
| 205. C73 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619405 | 2 |
| #22612898 | 2 |
| #22608490 | 2 |
| #22608427 | 2 |
| #22608325 | 2 |
| #22607832 | 2 |
| C73×#1286 | 2 |
| #9182 | 73 |