Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
364 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24907638 | C2 | semidirect |
| 3. #24906193 | C2 | semidirect |
| 6. #24905373 | C2 | semidirect |
| 7. C83×#1531 | C2 | semidirect |
| 159. #1531 | D83 | semidirect |
| 162. C83 | #10526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918846 | 2 |
| #24907638 | 2 |
| #24906193 | 2 |
| #24906186 | 2 |
| #24906073 | 2 |
| #24905373 | 2 |
| C83×#1531 | 2 |
| #10526 | 83 |