Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
560 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 5. C2×C4⋊#10596833 | C4 | semidirect |
| 13. #17988342 | C4 | semidirect |
| 14. #336×C73 | C4 | semidirect |
| 27. (C2×#64408)⋊C4 | C8 | semidirect |
| 173. C73 | #7028 | semidirect |
| 184. #336 | #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 |
| #22609688 | 2 |
| #7028 | 73 |