Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 111. #10596831 | #101 | semidirect |
| 137. C73 | #8165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556652 | 2 |
| #22625173 | 2 |
| #22625140 | 2 |
| #22624776 | 2 |
| C2×#17988711 | 2 |
| #8165 | 73 |