Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1154 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. #22625026 | C2 | direct (N × H) |
| 7. C2×#14556650 | C4 | semidirect |
| 11. C22×C4×Dic73 | C4 | semidirect |
| 13. #17988488 | C4 | semidirect |
| 15. C22×C4⋊C4×C73 | C4 | semidirect |
| 23. #14556650 | C2×C4 | semidirect |
| 40. C2×C4×Dic73 | C2×C4 | semidirect |
| 46. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 202. C2×C73 | #1393 | semidirect |
| 212. C73 | C2×#1393 | semidirect |
| 214. C22×C4⋊C4 | #64408 | semidirect |
| 242. C2×C4⋊C4 | C2×#64408 | semidirect |
| 413. C2 | #22625026 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556650 | 2 |
| #22625026 | 2 |
| C2×#17988488 | 2 |
| C2×#1393 | 73 |