Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22611725 | C2 | semidirect |
| 3. C2×#17988404 | C2 | semidirect |
| 4. C2×#17988402 | C2 | semidirect |
| 7. C73×#1388 | C2 | semidirect |
| 165. #1388 | D73 | semidirect |
| 166. C73 | #13390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988863 | 2 |
| #22611725 | 2 |
| C2×#17988404 | 2 |
| C2×#17988402 | 2 |
| #22611558 | 2 |
| #22609978 | 2 |
| C73×#1388 | 2 |
| #13390 | 73 |