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 |
|---|---|---|
| 2. C2×#19127956 | C2 | semidirect |
| 3. C2×#19127511 | C2 | semidirect |
| 4. #24909183 | C2 | semidirect |
| 5. C2×#19127482 | C2 | semidirect |
| 6. #24905569 | C2 | semidirect |
| 7. C2×#510×C83 | C2 | semidirect |
| 56. #14581724 | D4 | semidirect |
| 72. C2×Q16×C83 | D4 | semidirect |
| 79. M32×C83 | D4 | semidirect |
| 212. C2×#510 | D83 | semidirect |
| 219. C83 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D83 | semidirect |
| 283. M32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917068 | 2 |
| C2×#19127956 | 2 |
| C2×#19127511 | 2 |
| #24909183 | 2 |
| C2×#19127482 | 2 |
| #24905569 | 2 |
| C2×#510×C83 | 2 |
| #13317 | 83 |