Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
618 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 27. #17988325 | C4 | semidirect |
| 28. #17988324 | C4 | semidirect |
| 29. #17988323 | C4 | semidirect |
| 30. #328×C73 | C4 | semidirect |
| 116. C2×Dic146 | C4⋊C4 | semidirect |
| 139. C4⋊Dic73 | C4⋊C4 | semidirect |
| 146. C2×Q8×C73 | C4⋊C4 | semidirect |
| 151. C4⋊C4×C73 | C4⋊C4 | semidirect |
| 280. C73 | #8868 | semidirect |
| 303. #328 | #64408 | semidirect |
| 357. C2×Q8 | C4⋊#64408 | semidirect |
| 417. C4⋊C4 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626424 | 2 |
| #22625916 | 2 |
| #22625880 | 2 |
| #22625119 | 2 |
| #22624805 | 2 |
| #22624768 | 2 |
| #328×D73 | 2 |
| #8868 | 73 |