Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909688 | C2 | semidirect |
| 3. #24906849 | C2 | semidirect |
| 4. #24905510 | C2 | semidirect |
| 5. #24905424 | C2 | semidirect |
| 6. #24905417 | C2 | semidirect |
| 7. C83×#2224 | C2 | semidirect |
| 17. C4×C83⋊C16 | C22 | semidirect |
| 18. #19127454 | C22 | semidirect |
| 20. #500×C83 | C22 | semidirect |
| 23. C4⋊C16×C83 | C22 | semidirect |
| 83. D8×C83 | SD16 | semidirect |
| 154. #2224 | D83 | semidirect |
| 159. C83 | #12368 | semidirect |
| 162. #500 | C2×D83 | semidirect |
| 171. C4⋊C16 | C2×D83 | semidirect |
| 227. D8 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D332 | 2 |
| #24909688 | 2 |
| #24906849 | 2 |
| #24905510 | 2 |
| #24905424 | 2 |
| #24905417 | 2 |
| C83×#2224 | 2 |
| #12368 | 83 |