Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
654 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 16. #17988615 | C4 | semidirect |
| 17. #17988614 | C4 | semidirect |
| 18. #17988613 | C4 | semidirect |
| 21. #424×C73 | C4 | semidirect |
| 179. C73 | #11236 | semidirect |
| 191. #424 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626584 | 2 |
| #22625629 | 2 |
| #22625617 | 2 |
| #22625603 | 2 |
| #424×D73 | 2 |
| #11236 | 73 |