Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
310 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 8. #17989483 | C4 | semidirect |
| 13. #17988369 | C4 | semidirect |
| 15. #349×C73 | C4 | semidirect |
| 136. C73 | #7192 | semidirect |
| 146. #349 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626165 | 2 |
| #22625599 | 2 |
| #349×D73 | 2 |
| #7192 | 73 |