Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 44. #14556591 | C8 | semidirect |
| 47. #14556589 | C8 | semidirect |
| 51. C4⋊Q8×C73 | C8 | semidirect |
| 151. C4×C73 | Q8⋊C8 | semidirect |
| 155. Dic73 | Q8⋊C8 | semidirect |
| 169. C73 | #9673 | semidirect |
| 193. C4⋊Q8 | #10596842 | semidirect |
| 320. C4 | Q8⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#10596842 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C4⋊Q8×#64408 | 2 |
| #9673 | 73 |