Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 108 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. #22625041 | C2 | semidirect |
| 4. #22625040 | C2 | semidirect |
| 8. #17989520 | C4 | semidirect |
| 11. C2×#14556641 | C4 | semidirect |
| 15. #17988421 | C4 | semidirect |
| 17. C32×D73 | C4 | semidirect |
| 18. M64×C73 | C4 | semidirect |
| 87. C73 | #13551 | semidirect |
| 96. M64 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989520 | 2 |
| #22626139 | 2 |
| #22625041 | 2 |
| #22625040 | 2 |
| M64×D73 | 2 |
| #13551 | 73 |