Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C2×#17988325 | C2 | semidirect |
| 5. #22608296 | C2 | semidirect |
| 6. #22607773 | C2 | semidirect |
| 7. C73×#1298 | C2 | semidirect |
| 11. #17988918 | C4 | semidirect |
| 12. #17988901 | C4 | semidirect |
| 16. #17988745 | C4 | semidirect |
| 17. #17988728 | C4 | semidirect |
| 239. #1298 | D73 | semidirect |
| 241. C73 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620714 | 2 |
| #22618985 | 2 |
| #22608436 | 2 |
| C2×#17988325 | 2 |
| #22608296 | 2 |
| #22607773 | 2 |
| C73×#1298 | 2 |
| #9263 | 73 |