Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
606 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 37. C4⋊Q8×C73 | C8 | semidirect |
| 101. C4×C73 | Q8⋊C8 | semidirect |
| 120. C73 | #9637 | semidirect |
| 137. C4⋊Q8 | #10596833 | semidirect |
| 223. C4 | Q8⋊#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625863 | 2 |
| C42×#10596833 | 2 |
| C2×Q8⋊#10596833 | 2 |
| C4⋊Q8×Dic73 | 2 |
| #9637 | 73 |