Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
662 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14581735 | C2 | semidirect |
| 3. C2×#19127501 | C2 | semidirect |
| 4. #24905541 | C2 | semidirect |
| 5. C83×#1969 | C2 | semidirect |
| 36. C2×C83⋊C16 | D4 | semidirect |
| 41. C2×Q16×C83 | D4 | semidirect |
| 106. C2×C4×C83 | SD32 | semidirect |
| 148. #1969 | D83 | semidirect |
| 150. C83 | #13328 | semidirect |
| 171. C2×Q16 | D332 | semidirect |
| 256. C2×C4 | #14581735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581735 | 2 |
| C2×#19128078 | 2 |
| C2×#19127501 | 2 |
| #24905541 | 2 |
| C83×#1969 | 2 |
| #13328 | 83 |