Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 92 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. #17988408 | C4 | semidirect |
| 18. #17988407 | C4 | semidirect |
| 19. #364×C73 | C4 | semidirect |
| 120. C73 | #13187 | semidirect |
| 133. #364 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#365 | 2 |
| #22625868 | 2 |
| #22625733 | 2 |
| #22625003 | 2 |
| #364×D73 | 2 |
| #13187 | 73 |