Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1566 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 280 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. #22625828 | C2 | direct (N × H) |
| 13. C2×#14556548 | C4 | semidirect |
| 15. C22×#11924007 | C4 | semidirect |
| 17. C22×C4×Dic73 | C4 | semidirect |
| 18. C22×C42×C73 | C4 | semidirect |
| 36. C2×#11924007 | C2×C4 | semidirect |
| 43. C2×C4×Dic73 | C2×C4 | semidirect |
| 48. C2×C42×C73 | C2×C4 | semidirect |
| 149. C2×C73 | #1820 | semidirect |
| 158. C73 | C2×#1820 | semidirect |
| 168. C22×C42 | #64408 | semidirect |
| 201. C2×C42 | C2×#64408 | semidirect |
| 304. C2 | #22625828 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989530 | 2 |
| #22625828 | 2 |
| C2×#17989465 | 2 |
| C22×#14556548 | 2 |
| C2×#1820 | 73 |