Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 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 |
|---|---|---|
| 1. #24909247 | C2 | semidirect |
| 5. #24905577 | C2 | semidirect |
| 6. #24905564 | C2 | semidirect |
| 7. C83×#1382 | C2 | semidirect |
| 142. #1382 | D83 | semidirect |
| 143. C83 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909247 | 2 |
| C2×#19127484 | 2 |
| #24907518 | 2 |
| #24907506 | 2 |
| #24905577 | 2 |
| #24905564 | 2 |
| C83×#1382 | 2 |
| #13500 | 83 |