Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#17988420 | C2 | semidirect |
| 3. M64×D73 | C2 | semidirect |
| 4. #22608074 | C2 | semidirect |
| 5. #22608073 | C2 | semidirect |
| 6. #22608072 | C2 | semidirect |
| 7. C73×#1401 | C2 | semidirect |
| 18. #17988421 | C22 | semidirect |
| 22. C2×#14556497 | C22 | semidirect |
| 25. M64×C73 | C22 | semidirect |
| 26. C2×C32×C73 | C22 | semidirect |
| 150. #1401 | D73 | semidirect |
| 151. C73 | #13558 | semidirect |
| 167. M64 | C2×D73 | semidirect |
| 170. C2×C32 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #504×D73 | 2 |
| C2×#17988420 | 2 |
| M64×D73 | 2 |
| #22608074 | 2 |
| #22608073 | 2 |
| #22608072 | 2 |
| C73×#1401 | 2 |
| #13558 | 73 |