Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #22622937 | C2 | semidirect |
| 4. #22607979 | C2 | semidirect |
| 5. Q8⋊#11924003 | C2 | semidirect |
| 6. #22607894 | C2 | semidirect |
| 91. Q8×C73 | SD32 | semidirect |
| 140. C73 | #12330 | semidirect |
| 228. Q8 | #14556535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622937 | 2 |
| #22612186 | 2 |
| #22611968 | 2 |
| #22607979 | 2 |
| Q8⋊#11924003 | 2 |
| #22607894 | 2 |
| C73×#1668 | 2 |
| #12330 | 73 |