Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 64. C2×Dic146 | Q16 | semidirect |
| 78. C4⋊Dic73 | Q16 | semidirect |
| 192. C73 | #7784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617890 | 2 |
| #22611256 | 2 |
| #22611069 | 2 |
| #22607757 | 2 |
| #22607756 | 2 |
| #22607755 | 2 |
| C73×#2016 | 2 |
| #7784 | 73 |