Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 5. C22⋊#11924031 | C4 | semidirect |
| 52. C22×C4×C73 | C16 | semidirect |
| 130. C73 | #7183 | semidirect |
| 167. C22×C4 | #11924031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11924031 | 2 |
| C2×#17988342 | 2 |
| #7183 | 73 |