Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
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×#19127534 | C2 | semidirect |
| 3. M64×D83 | C2 | semidirect |
| 4. #24905606 | C2 | semidirect |
| 5. #24905605 | C2 | semidirect |
| 6. #24905604 | C2 | semidirect |
| 7. C83×#1401 | C2 | semidirect |
| 18. #19127535 | C22 | semidirect |
| 22. C2×C83⋊C32 | C22 | semidirect |
| 25. M64×C83 | C22 | semidirect |
| 26. C2×C32×C83 | C22 | semidirect |
| 150. #1401 | D83 | semidirect |
| 151. C83 | #13558 | semidirect |
| 167. M64 | C2×D83 | semidirect |
| 170. C2×C32 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #504×D83 | 2 |
| C2×#19127534 | 2 |
| M64×D83 | 2 |
| #24905606 | 2 |
| #24905605 | 2 |
| #24905604 | 2 |
| C83×#1401 | 2 |
| #13558 | 83 |