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. #22625025 | C2 | direct (N × H) |
| 7. C2×#14556650 | C4 | semidirect |
| 10. C22×C4⋊Dic73 | C4 | semidirect |
| 13. #17988489 | C4 | semidirect |
| 15. C22×C42×C73 | C4 | semidirect |
| 23. #14556650 | C2×C4 | semidirect |
| 38. C2×C4⋊Dic73 | C2×C4 | semidirect |
| 46. C2×C42×C73 | C2×C4 | semidirect |
| 202. C2×C73 | #1393 | semidirect |
| 212. C73 | C2×#1393 | semidirect |
| 217. C22×C42 | #64408 | semidirect |
| 252. C2×C42 | C2×#64408 | semidirect |
| 413. C2 | #22625025 | 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 |
| #22625025 | 2 |
| C2×#17988489 | 2 |
| C2×#1393 | 73 |