Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22611490 | C2 | semidirect |
| 3. #22611339 | C2 | semidirect |
| 5. #22607753 | C2 | semidirect |
| 7. C73×#1272 | C2 | semidirect |
| 196. #1272 | D73 | semidirect |
| 199. C73 | #7787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22616949 | 2 |
| #22611490 | 2 |
| #22611339 | 2 |
| #22611336 | 2 |
| #22607753 | 2 |
| #22607751 | 2 |
| C73×#1272 | 2 |
| #7787 | 73 |