Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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×#19128142 | C2 | semidirect |
| 3. #24909397 | C2 | semidirect |
| 4. #24909380 | C2 | semidirect |
| 5. #24909183 | C2 | semidirect |
| 6. #24909074 | C2 | semidirect |
| 7. C23×Q16×C83 | C2 | semidirect |
| 11. C2×#14581738 | C22 | semidirect |
| 12. C2×#14581735 | C22 | semidirect |
| 19. #19127505 | C22 | semidirect |
| 61. C2×Q16×C83 | D4 | semidirect |
| 153. C22×C83 | #510 | semidirect |
| 170. C23×Q16 | D83 | semidirect |
| 177. C83 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D83 | semidirect |
| 325. C22 | #19128142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128142 | 2 |
| #24917044 | 2 |
| #24909397 | 2 |
| #24909380 | 2 |
| #24909183 | 2 |
| #24909074 | 2 |
| C23×Q16×C83 | 2 |
| #33518 | 83 |