Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #22610484 | C2 | semidirect |
| 5. #22610219 | C2 | semidirect |
| 6. #22608059 | C2 | semidirect |
| 7. C73×#2129 | C2 | semidirect |
| 196. #2129 | D73 | semidirect |
| 202. C73 | #13433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620798 | 2 |
| #22611580 | 2 |
| #22610484 | 2 |
| #22610456 | 2 |
| #22610219 | 2 |
| #22608059 | 2 |
| C73×#2129 | 2 |
| #13433 | 73 |