Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 11. C2×#14556591 | C4 | semidirect |
| 16. #17988486 | C4 | semidirect |
| 19. #384×C73 | C4 | semidirect |
| 29. (C2×#64408)⋊C4 | Q8 | semidirect |
| 184. C73 | #9908 | semidirect |
| 194. #384 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625786 | 2 |
| C4×(C2×#64408)⋊C4 | 2 |
| #22624804 | 2 |
| #22618284 | 2 |
| #9908 | 73 |