Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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. #24907079 | C2 | semidirect |
| 4. #24905532 | C2 | semidirect |
| 5. #24905513 | C2 | semidirect |
| 6. #24905512 | C2 | semidirect |
| 95. C83⋊C8 | SD32 | semidirect |
| 120. C83 | #12426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909508 | 2 |
| #24907079 | 2 |
| D8×C83⋊C8 | 2 |
| #24905532 | 2 |
| #24905513 | 2 |
| #24905512 | 2 |
| C83×#2208 | 2 |
| #12426 | 83 |