Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
182 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22625097 | C2 | semidirect |
| 4. #22625096 | C2 | semidirect |
| 14. #17988421 | C4 | semidirect |
| 16. C32×D73 | C4 | semidirect |
| 17. M64×C73 | C4 | semidirect |
| 86. C73 | #13638 | semidirect |
| 92. M64 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989516 | 2 |
| #22626282 | 2 |
| #22625097 | 2 |
| #22625096 | 2 |
| M64×D73 | 2 |
| #13638 | 73 |