Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 1. #24909600 | C2 | semidirect |
| 2. #24907052 | C2 | semidirect |
| 3. D8×C83⋊C8 | C2 | semidirect |
| 4. #24905526 | C2 | semidirect |
| 5. #24905517 | C2 | semidirect |
| 6. #24905509 | C2 | semidirect |
| 65. D8×C83 | SD16 | semidirect |
| 96. C83⋊C8 | D16 | semidirect |
| 124. C83 | #12416 | semidirect |
| 174. D8 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909600 | 2 |
| #24907052 | 2 |
| D8×C83⋊C8 | 2 |
| #24905526 | 2 |
| #24905517 | 2 |
| #24905509 | 2 |
| C83×#2206 | 2 |
| #12416 | 83 |