Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
878 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 878 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 |
|---|---|---|
| 1. #22620728 | C2 | semidirect |
| 2. C2×#17988721 | C2 | semidirect |
| 3. #22609852 | C2 | semidirect |
| 4. #22608291 | C2 | semidirect |
| 5. #22608290 | C2 | semidirect |
| 6. #22607819 | C2 | semidirect |
| 7. C2×#447×C73 | C2 | semidirect |
| 243. C2×#447 | D73 | semidirect |
| 248. C73 | #9986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620728 | 2 |
| C2×#17988721 | 2 |
| #22609852 | 2 |
| #22608291 | 2 |
| #22608290 | 2 |
| #22607819 | 2 |
| C2×#447×C73 | 2 |
| #9986 | 73 |