Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
770 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #22610917 | C2 | semidirect |
| 4. #22609866 | C2 | semidirect |
| 6. #22607777 | C2 | semidirect |
| 7. C2×#451×C73 | C2 | semidirect |
| 232. C2×#451 | D73 | semidirect |
| 238. C73 | #9956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620684 | 2 |
| #22613585 | 2 |
| #22610917 | 2 |
| #22609866 | 2 |
| #22608500 | 2 |
| #22607777 | 2 |
| C2×#451×C73 | 2 |
| #9956 | 73 |