Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 13. #17988991 | C4 | semidirect |
| 14. #17988965 | C4 | semidirect |
| 19. C4×Dic292 | C4 | semidirect |
| 22. C4×Q16×C73 | C4 | semidirect |
| 148. C73 | #11743 | semidirect |
| 158. C4×Q16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626290 | 2 |
| C4×#14556660 | 2 |
| #22624920 | 2 |
| #22624919 | 2 |
| #22620514 | 2 |
| #11743 | 73 |