Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
186 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 22 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. #22625063 | C2 | semidirect |
| 5. #17988964 | C4 | semidirect |
| 7. C82×C73 | C4 | semidirect |
| 53. C73 | #7529 | semidirect |
| 58. C82 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625063 | 2 |
| #22609546 | 2 |
| #7529 | 73 |