Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1062 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 288 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. #22625859 | C2 | semidirect |
| 2. #22625858 | C2 | semidirect |
| 50. C4×Dic73 | M16 | semidirect |
| 58. C42×C73 | M16 | semidirect |
| 102. C73 | #20772 | semidirect |
| 156. C42 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625859 | 2 |
| #22625858 | 2 |
| #22625594 | 2 |
| C2×C42×Dic73 | 2 |
| #20772 | 73 |