Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 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×D1328 | C2 | semidirect |
| 2. C2×#19127972 | C2 | semidirect |
| 3. #24917112 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. #24909178 | C2 | semidirect |
| 6. C2×#19127484 | C2 | semidirect |
| 7. C83×#1382 | C2 | semidirect |
| 47. C2×D664 | D4 | semidirect |
| 70. C2×C16×C83 | D4 | semidirect |
| 72. #108×C83 | D4 | semidirect |
| 206. #1382 | D83 | semidirect |
| 207. C83 | #13319 | semidirect |
| 268. C2×C16 | D332 | semidirect |
| 270. #108 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1328 | 2 |
| C2×#19127972 | 2 |
| #24917112 | 2 |
| C2×#19127513 | 2 |
| #24909178 | 2 |
| C2×#19127484 | 2 |
| C83×#1382 | 2 |
| #13319 | 83 |