Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24909072 | C2 | semidirect |
| 3. #341×D83 | C2 | semidirect |
| 4. #24905481 | C2 | semidirect |
| 5. #24905479 | C2 | semidirect |
| 6. #24905477 | C2 | semidirect |
| 7. C83×#1350 | C2 | semidirect |
| 186. #1350 | D83 | semidirect |
| 189. C83 | #11710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917046 | 2 |
| #24909072 | 2 |
| #341×D83 | 2 |
| #24905481 | 2 |
| #24905479 | 2 |
| #24905477 | 2 |
| C83×#1350 | 2 |
| #11710 | 83 |