Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 89. C2×Q8×C73 | Q16 | semidirect |
| 109. C4⋊C4×C73 | Q16 | semidirect |
| 192. C73 | #7784 | semidirect |
| 259. C2×Q8 | #11924018 | semidirect |
| 294. C4⋊C4 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611259 | 2 |
| #22611072 | 2 |
| #22611030 | 2 |
| #22607757 | 2 |
| #22607754 | 2 |
| C73×#2806 | 2 |
| #7784 | 73 |