Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#14581736 | C2 | semidirect |
| 2. C2×#19127976 | C2 | semidirect |
| 3. C2×#19127514 | C2 | semidirect |
| 4. #24909182 | C2 | semidirect |
| 5. C2×#19127485 | C2 | semidirect |
| 6. #24905558 | C2 | semidirect |
| 37. C2×Dic332 | D4 | semidirect |
| 47. C2×C83⋊C16 | D4 | semidirect |
| 49. #14581728 | D4 | semidirect |
| 202. C83 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581736 | 2 |
| C2×#19127976 | 2 |
| C2×#19127514 | 2 |
| #24909182 | 2 |
| C2×#19127485 | 2 |
| #24905558 | 2 |
| C83×#3058 | 2 |
| #13321 | 83 |