Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 17. #368×C73 | C4 | semidirect |
| 101. C73 | #13171 | semidirect |
| 108. #368 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988413 | 2 |
| #22611527 | 2 |
| #22610717 | 2 |
| #22608041 | 2 |
| C2×#368×C73 | 2 |
| #13171 | 73 |