Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1202 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 355 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. #24910384 | C2 | semidirect |
| 3. #24906024 | C2 | semidirect |
| 4. #24905959 | C2 | semidirect |
| 5. C83×#2982 | C2 | semidirect |
| 7. #19128373 | C4 | semidirect |
| 8. Q8×D332 | C4 | semidirect |
| 128. #2982 | D83 | semidirect |
| 132. C83 | #17618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921234 | 2 |
| #24910384 | 2 |
| #24906024 | 2 |
| #24905959 | 2 |
| C83×#2982 | 2 |
| #17618 | 83 |