Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22608443 | C2 | semidirect |
| 4. #22607825 | C2 | semidirect |
| 17. #489×C73 | C4 | semidirect |
| 38. C4⋊Q8×C73 | C2×C4 | semidirect |
| 50. #97×C73 | C2×C4 | semidirect |
| 147. C73 | #9439 | semidirect |
| 150. #489 | Dic73 | semidirect |
| 168. C4⋊Q8 | C2×Dic73 | semidirect |
| 188. #97 | C2×Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613043 | 2 |
| #22608555 | 2 |
| #22608443 | 2 |
| #22607825 | 2 |
| C73×#3140 | 2 |
| #9439 | 73 |