Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 8. C4⋊#11924031 | C4 | semidirect |
| 12. C4⋊#11924003 | C4 | semidirect |
| 15. C4⋊C16×C73 | C4 | semidirect |
| 98. C73 | #7150 | semidirect |
| 106. C4⋊C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626291 | 2 |
| #22625587 | 2 |
| #22611733 | 2 |
| #7150 | 73 |