Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
528 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 24. C4⋊#10596842 | Q8 | semidirect |
| 42. #14556591 | C8 | semidirect |
| 44. #14556590 | C8 | semidirect |
| 49. C4⋊Q8×C73 | C8 | semidirect |
| 166. C73 | #9864 | semidirect |
| 189. 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 |
| #22626939 | 2 |
| C4⋊Q8×#64408 | 2 |
| #9864 | 73 |