Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22619880 | C2 | semidirect |
| 4. #22610000 | C2 | semidirect |
| 5. #22608296 | C2 | semidirect |
| 7. C73×#1293 | C2 | semidirect |
| 210. #1293 | D73 | semidirect |
| 211. C73 | #9978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620689 | 2 |
| #22619880 | 2 |
| #22619872 | 2 |
| #22610000 | 2 |
| #22608296 | 2 |
| #22608292 | 2 |
| C73×#1293 | 2 |
| #9978 | 73 |