Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
530 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 34. #14556591 | C8 | semidirect |
| 36. #14556589 | C8 | semidirect |
| 39. C4⋊Q8×C73 | C8 | semidirect |
| 126. C73 | #9641 | semidirect |
| 145. C4⋊Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627073 | 2 |
| #22627065 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C4⋊Q8×#64408 | 2 |
| #9641 | 73 |