Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
268 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909712 | C2 | semidirect |
| 2. D4×C83⋊C16 | C2 | semidirect |
| 3. #24906818 | C2 | semidirect |
| 4. #24905534 | C2 | semidirect |
| 5. #24905509 | C2 | semidirect |
| 6. #24905508 | C2 | semidirect |
| 7. C83×#1667 | C2 | semidirect |
| 56. C83⋊C16 | D8 | semidirect |
| 84. D4×C83 | D16 | semidirect |
| 128. #1667 | D83 | semidirect |
| 132. C83 | #12430 | semidirect |
| 214. D4 | #14581733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909712 | 2 |
| D4×C83⋊C16 | 2 |
| #24906818 | 2 |
| #24905534 | 2 |
| #24905509 | 2 |
| #24905508 | 2 |
| C83×#1667 | 2 |
| #12430 | 83 |