Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 126 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. #22625037 | C2 | semidirect |
| 4. C32×#64408 | C2 | semidirect |
| 8. #17989518 | C4 | semidirect |
| 11. C2×#14556641 | C4 | semidirect |
| 15. #17988421 | C4 | semidirect |
| 16. #17988420 | C4 | semidirect |
| 18. M64×C73 | C4 | semidirect |
| 87. C73 | #13549 | semidirect |
| 93. M64 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| #22626139 | 2 |
| #22625037 | 2 |
| C32×#64408 | 2 |
| M64×D73 | 2 |
| #13549 | 73 |