Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22610900 | C2 | semidirect |
| 4. #22610100 | C2 | semidirect |
| 5. C2×#17988328 | C2 | semidirect |
| 7. C73×#1295 | C2 | semidirect |
| 216. #1295 | D73 | semidirect |
| 217. C73 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617983 | 2 |
| #22610900 | 2 |
| #22610747 | 2 |
| #22610100 | 2 |
| C2×#17988328 | 2 |
| C2×#17988326 | 2 |
| C73×#1295 | 2 |
| #10427 | 73 |