Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 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. #17988987 | C4 | semidirect |
| 127. C73 | #13273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988987 | 2 |
| C2×#17988407 | 2 |
| #22609813 | 2 |
| #22608038 | 2 |
| #22608037 | 2 |
| #22608031 | 2 |
| C73×#1383 | 2 |
| #13273 | 73 |