Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14581737 | C2 | semidirect |
| 2. C2×#19127977 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. #24909182 | C2 | semidirect |
| 6. C2×#19127484 | C2 | semidirect |
| 7. C83×#1382 | C2 | semidirect |
| 40. C2×Dic332 | D4 | semidirect |
| 70. C2×C16×C83 | D4 | semidirect |
| 72. #108×C83 | D4 | semidirect |
| 201. #1382 | D83 | semidirect |
| 202. C83 | #13321 | semidirect |
| 263. C2×C16 | D332 | semidirect |
| 265. #108 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581737 | 2 |
| C2×#19127977 | 2 |
| #24917112 | 2 |
| C2×#19127513 | 2 |
| #24909182 | 2 |
| C2×#19127484 | 2 |
| C83×#1382 | 2 |
| #13321 | 83 |