Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1230 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 224 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. #22626215 | C2 | direct (N × H) |
| 3. C2×#17989494 | C2 | semidirect |
| 10. #17989494 | C22 | semidirect |
| 12. C23×Dic146 | C4 | semidirect |
| 14. #17989163 | C4 | semidirect |
| 16. C2×#14556591 | C4 | semidirect |
| 20. C2×#117×C73 | C4 | semidirect |
| 40. C22×Dic146 | C2×C4 | semidirect |
| 46. #14556591 | C2×C4 | semidirect |
| 58. #117×C73 | C2×C4 | semidirect |
| 188. C2×C73 | #2129 | semidirect |
| 196. C73 | C2×#2129 | semidirect |
| 207. C2×#117 | #64408 | semidirect |
| 242. #117 | C2×#64408 | semidirect |
| 381. C2 | #22626215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989566 | 2 |
| #22626215 | 2 |
| C2×#17989494 | 2 |
| C2×#17989163 | 2 |
| C2×#2129 | 73 |