Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 12. #17988967 | C4 | semidirect |
| 17. #17988681 | C4 | semidirect |
| 19. #500×C73 | C4 | semidirect |
| 125. C73 | #11743 | semidirect |
| 127. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626291 | 2 |
| C4×#14556660 | 2 |
| #22624920 | 2 |
| #22620518 | 2 |
| #11743 | 73 |