Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 3. #22624749 | C2 | semidirect |
| 44. C2×C4⋊C4×C73 | C8 | semidirect |
| 165. C73 | #7593 | semidirect |
| 196. C2×C4⋊C4 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625821 | 2 |
| #22624749 | 2 |
| C2×#17988486 | 2 |
| #7593 | 73 |