Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #22625061 | C2 | direct (N × H) |
| 13. C2×#14556591 | C4 | semidirect |
| 17. #17988981 | C4 | semidirect |
| 19. C2×#97×C73 | C4 | semidirect |
| 39. #14556591 | C2×C4 | semidirect |
| 50. #97×C73 | C2×C4 | semidirect |
| 149. C2×C73 | #1407 | semidirect |
| 157. C73 | C2×#1407 | semidirect |
| 168. C2×#97 | #64408 | semidirect |
| 203. #97 | C2×#64408 | semidirect |
| 303. C2 | #22625061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989496 | 2 |
| C2×#17989494 | 2 |
| #22625061 | 2 |
| C2×#17988981 | 2 |
| C2×#1407 | 73 |