Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
626 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 180 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. #22626030 | C2 | semidirect |
| 3. #22625986 | C2 | semidirect |
| 5. #22625865 | C2 | semidirect |
| 6. #22625860 | C2 | semidirect |
| 123. C73 | #23381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626030 | 2 |
| #22626003 | 2 |
| #22625986 | 2 |
| #22625879 | 2 |
| #22625865 | 2 |
| #22625860 | 2 |
| #22613234 | 2 |
| #23381 | 73 |