Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24909262 | C2 | semidirect |
| 3. #24905417 | C2 | semidirect |
| 4. C83×#2163 | C2 | semidirect |
| 15. C4×C83⋊C16 | C22 | semidirect |
| 17. C4⋊C16×C83 | C22 | semidirect |
| 128. #2163 | D83 | semidirect |
| 131. C83 | #11631 | semidirect |
| 142. C4⋊C16 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D332 | 2 |
| #24909262 | 2 |
| #24905417 | 2 |
| C83×#2163 | 2 |
| #11631 | 83 |