Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 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. #22611715 | C2 | semidirect |
| 3. #22608119 | C2 | semidirect |
| 4. C2×M64×C73 | C2 | semidirect |
| 8. #17989019 | C4 | semidirect |
| 10. C2×Dic584 | C4 | semidirect |
| 12. C2×D1168 | C4 | semidirect |
| 14. #17988415 | C22 | semidirect |
| 18. M64×C73 | C22 | semidirect |
| 114. C2×M64 | D73 | semidirect |
| 117. C73 | #13622 | semidirect |
| 129. M64 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989019 | 2 |
| #22611715 | 2 |
| #22608119 | 2 |
| C2×M64×C73 | 2 |
| #13622 | 73 |