Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #22621314 | C2 | semidirect |
| 3. #22609071 | C2 | semidirect |
| 4. #22609052 | C2 | semidirect |
| 5. #22609009 | C2 | semidirect |
| 6. #22608990 | C2 | semidirect |
| 7. #22608666 | C2 | semidirect |
| 8. #22608386 | C2 | semidirect |
| 9. C73×#3550 | C2 | semidirect |
| 191. #3550 | D73 | semidirect |
| 200. C73 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621314 | 2 |
| #22620357 | 2 |
| #22609071 | 2 |
| #22609052 | 2 |
| #22609009 | 2 |
| #22608990 | 2 |
| #22608666 | 2 |
| #22608386 | 2 |
| C73×#3550 | 2 |
| #18688 | 73 |