Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
506 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 142 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. #22625136 | C2 | semidirect |
| 4. #22624770 | C2 | semidirect |
| 26. C2×#11924037 | C8 | semidirect |
| 30. C22×#10596833 | C8 | semidirect |
| 163. C73 | #8156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989551 | 2 |
| #22625163 | 2 |
| #22625136 | 2 |
| #22624770 | 2 |
| #22608242 | 2 |
| #8156 | 73 |