Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24906028 | C2 | semidirect |
| 4. #24905961 | C2 | semidirect |
| 6. #24905323 | C2 | semidirect |
| 7. C83×#1303 | C2 | semidirect |
| 12. #19127992 | C4 | semidirect |
| 13. #19127982 | C4 | semidirect |
| 32. #14581792 | C2×C4 | semidirect |
| 33. #14581792 | C2×C4 | semidirect |
| 67. C4⋊C8×C83 | C2×C4 | semidirect |
| 201. #1303 | D83 | semidirect |
| 203. C83 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917262 | 2 |
| #24910374 | 2 |
| #24906028 | 2 |
| #24905961 | 2 |
| #24905855 | 2 |
| #24905323 | 2 |
| C83×#1303 | 2 |
| #9175 | 83 |