Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22624925 | C2 | semidirect |
| 4. #22624912 | C2 | semidirect |
| 12. C2×C4×Dic146 | C4 | semidirect |
| 15. #17988514 | C4 | semidirect |
| 18. #17988500 | C4 | semidirect |
| 22. #376×C73 | C4 | semidirect |
| 184. C73 | #11728 | semidirect |
| 198. #376 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556650 | 2 |
| #22625168 | 2 |
| #22624925 | 2 |
| #22624912 | 2 |
| #22613217 | 2 |
| #11728 | 73 |