Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 9. C4×#11924031 | C4 | semidirect |
| 13. C4⋊#11924003 | C4 | semidirect |
| 15. C4⋊C16×C73 | C4 | semidirect |
| 114. C73 | #7168 | semidirect |
| 123. C4⋊C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| #22625725 | 2 |
| #22611685 | 2 |
| #7168 | 73 |