Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 26. C22⋊#10596831 | Q8 | semidirect |
| 30. #14556498 | Q8 | semidirect |
| 194. C73 | #10569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610118 | 2 |
| #22608187 | 2 |
| #22607809 | 2 |
| #22607774 | 2 |
| C73×#2659 | 2 |
| #10569 | 73 |