Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
506 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22607953 | C2 | semidirect |
| 4. #22607932 | C2 | semidirect |
| 6. C2×#14556570 | C4 | semidirect |
| 7. #17988512 | C4 | semidirect |
| 9. #17988499 | C4 | semidirect |
| 16. C4×C22⋊Dic73 | C4 | semidirect |
| 205. C73 | #11845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615089 | 2 |
| #22610005 | 2 |
| #22607953 | 2 |
| #22607932 | 2 |
| C2×#323×C73 | 2 |
| #11845 | 73 |