Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24906833 | C2 | semidirect |
| 4. #24905537 | C2 | semidirect |
| 5. #24905513 | C2 | semidirect |
| 7. Q8×C16×C83 | C2 | semidirect |
| 70. C16×C83 | SD16 | semidirect |
| 73. Q8×C83 | SD32 | semidirect |
| 111. Q8×C16 | D83 | semidirect |
| 117. C83 | #12441 | semidirect |
| 180. C16 | #13050577 | semidirect |
| 185. Q8 | #14581737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909719 | 2 |
| #24906833 | 2 |
| #24906823 | 2 |
| #24905537 | 2 |
| #24905513 | 2 |
| #24905510 | 2 |
| Q8×C16×C83 | 2 |
| #12441 | 83 |