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. #22625060 | C2 | direct (N × H) |
| 16. #17988979 | C4 | semidirect |
| 18. C2×#14556502 | C4 | semidirect |
| 19. C2×C4⋊Q8×C73 | C4 | semidirect |
| 44. #14556502 | C2×C4 | semidirect |
| 48. C4⋊Q8×C73 | C2×C4 | semidirect |
| 149. C2×C73 | #1407 | semidirect |
| 157. C73 | C2×#1407 | semidirect |
| 160. C2×C4⋊Q8 | #64408 | semidirect |
| 188. C4⋊Q8 | C2×#64408 | semidirect |
| 303. C2 | #22625060 | 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 |
| #22625060 | 2 |
| C2×#17988979 | 2 |
| C2×#1407 | 73 |