Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626834 | C2 | semidirect |
| 3. #22625273 | C2 | semidirect |
| 5. #22624796 | C2 | semidirect |
| 6. #22624776 | C2 | semidirect |
| 217. C73 | #9244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626834 | 2 |
| #22625392 | 2 |
| #22625273 | 2 |
| #22625202 | 2 |
| #22624796 | 2 |
| #22624776 | 2 |
| C2×#17988811 | 2 |
| #9244 | 73 |