Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
596 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 127 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. #24907316 | C2 | semidirect |
| 3. C2×#19127440 | C2 | semidirect |
| 4. C83×#1745 | C2 | semidirect |
| 48. #97×C83 | D4 | semidirect |
| 164. #1745 | D83 | semidirect |
| 166. C83 | #9689 | semidirect |
| 210. #97 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915820 | 2 |
| #24907316 | 2 |
| C2×#19127440 | 2 |
| C83×#1745 | 2 |
| #9689 | 83 |