Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. #17988984 | C4 | semidirect |
| 33. #14556525 | Q8 | semidirect |
| 49. #108×C73 | Q8 | semidirect |
| 129. C73 | #13272 | semidirect |
| 162. #108 | Dic146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988984 | 2 |
| C2×#17988407 | 2 |
| #22609813 | 2 |
| #22608038 | 2 |
| #22608037 | 2 |
| #22608031 | 2 |
| C73×#1383 | 2 |
| #13272 | 73 |