Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
528 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 165 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. Q8×Dic332 | C2 | semidirect |
| 3. #24909687 | C2 | semidirect |
| 4. #24909611 | C2 | semidirect |
| 5. #24909504 | C2 | semidirect |
| 6. C4×#14581737 | C2 | semidirect |
| 7. Q8×C16×C83 | C2 | semidirect |
| 54. Dic332 | #41 | semidirect |
| 72. Q8×C83 | SD32 | semidirect |
| 111. Q8×C16 | D83 | semidirect |
| 113. C83 | #33929 | semidirect |
| 181. Q8 | #14581737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920438 | 2 |
| Q8×Dic332 | 2 |
| #24909687 | 2 |
| #24909611 | 2 |
| #24909504 | 2 |
| C4×#14581737 | 2 |
| Q8×C16×C83 | 2 |
| #33929 | 83 |