Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
566 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19128141 | C2 | semidirect |
| 2. C22×#14581736 | C2 | semidirect |
| 3. C2×#19127514 | C2 | semidirect |
| 4. C2×#19127508 | C2 | semidirect |
| 5. #24908378 | C2 | semidirect |
| 6. #24905552 | C2 | semidirect |
| 37. C2×Dic332 | D4 | semidirect |
| 43. #14581732 | D4 | semidirect |
| 47. C2×C83⋊C16 | D4 | semidirect |
| 209. C83 | #13338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128141 | 2 |
| C22×#14581736 | 2 |
| C2×#19127514 | 2 |
| C2×#19127508 | 2 |
| #24908378 | 2 |
| #24905552 | 2 |
| C83×#3155 | 2 |
| #13338 | 83 |