Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 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. #22611704 | C2 | semidirect |
| 3. #22611651 | C2 | semidirect |
| 6. #22608047 | C2 | semidirect |
| 7. C73×#2141 | C2 | semidirect |
| 163. #2141 | D73 | semidirect |
| 167. C73 | #13405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988859 | 2 |
| #22611704 | 2 |
| #22611651 | 2 |
| #22611558 | 2 |
| #22609974 | 2 |
| #22608047 | 2 |
| C73×#2141 | 2 |
| #13405 | 73 |