Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
384 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 1. C4×#14556660 | C2 | semidirect |
| 2. #22625492 | C2 | semidirect |
| 4. #22624783 | C2 | semidirect |
| 15. Q8×#10596831 | C4 | semidirect |
| 16. #17988666 | C4 | semidirect |
| 19. #17988652 | C4 | semidirect |
| 24. #446×C73 | C4 | semidirect |
| 162. C73 | #8697 | semidirect |
| 164. #446 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556660 | 2 |
| #22625492 | 2 |
| #22625335 | 2 |
| #22624783 | 2 |
| #22618905 | 2 |
| #8697 | 73 |