Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
344 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909692 | C2 | semidirect |
| 4. #24905513 | C2 | semidirect |
| 5. #24905427 | C2 | semidirect |
| 7. C83×#2227 | C2 | semidirect |
| 135. #2227 | D83 | semidirect |
| 140. C83 | #12374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D332 | 2 |
| #24909692 | 2 |
| #24906859 | 2 |
| #24905513 | 2 |
| #24905427 | 2 |
| #24905417 | 2 |
| C83×#2227 | 2 |
| #12374 | 83 |