Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22625871 | C2 | semidirect |
| 2. #22625473 | C2 | semidirect |
| 4. #22624800 | C2 | semidirect |
| 186. C73 | #8682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625871 | 2 |
| #22625473 | 2 |
| #22625442 | 2 |
| #22624800 | 2 |
| #22618638 | 2 |
| #8682 | 73 |