Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
530 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24907634 | C2 | semidirect |
| 3. #24906136 | C2 | semidirect |
| 4. #24906134 | C2 | semidirect |
| 6. #24905747 | C2 | semidirect |
| 163. C83 | #9768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128073 | 2 |
| #24907634 | 2 |
| #24906136 | 2 |
| #24906134 | 2 |
| #24906131 | 2 |
| #24905747 | 2 |
| C83×#1545 | 2 |
| #9768 | 83 |