Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 45. #117×C73 | C8 | semidirect |
| 152. C73 | #11454 | semidirect |
| 173. #117 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625162 | 2 |
| #22624875 | 2 |
| #22612554 | 2 |
| #11454 | 73 |