Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1198 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 1. C2×C22⋊#11924040 | C2 | semidirect |
| 3. C22×#11924040 | C22 | semidirect |
| 40. C24×C73 | C16 | semidirect |
| 66. C22×C73 | C22⋊C16 | semidirect |
| 80. C73 | #12679 | semidirect |
| 102. C24 | #11924040 | semidirect |
| 144. C22 | C22⋊#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11924040 | 2 |
| C24×#10596833 | 2 |
| #12679 | 73 |