Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 2. #22609956 | C2 | semidirect |
| 3. #22607944 | C2 | semidirect |
| 4. #22607941 | C2 | semidirect |
| 5. C2×C22⋊C16×C73 | C2 | semidirect |
| 6. C2×#14556613 | C4 | semidirect |
| 8. #17988828 | C4 | semidirect |
| 10. #17988823 | C4 | semidirect |
| 14. #17988625 | C4 | semidirect |
| 173. C2×C22⋊C16 | D73 | semidirect |
| 177. C73 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619512 | 2 |
| #22609956 | 2 |
| #22607944 | 2 |
| #22607941 | 2 |
| C2×C22⋊C16×C73 | 2 |
| #11885 | 73 |