Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 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. #22611703 | C2 | semidirect |
| 3. C2×#17988404 | C2 | semidirect |
| 4. #22611650 | C2 | semidirect |
| 7. C73×#1384 | C2 | semidirect |
| 166. #1384 | D73 | semidirect |
| 167. C73 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619587 | 2 |
| #22611703 | 2 |
| C2×#17988404 | 2 |
| #22611650 | 2 |
| #22611560 | 2 |
| #22609982 | 2 |
| C73×#1384 | 2 |
| #13397 | 73 |