Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
582 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. #24909710 | C2 | semidirect |
| 4. #24909709 | C2 | semidirect |
| 5. #24909708 | C2 | semidirect |
| 6. #24909707 | C2 | semidirect |
| 9. C83×#2245 | C2 | semidirect |
| 145. D83 | #2245 | direct (N × H) |
| 152. #2245 | D83 | direct (N × H) |
| 155. C83 | C2×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D83 | 2 |
| #494×D83 | 2 |
| #24909710 | 2 |
| #24909709 | 2 |
| #24909708 | 2 |
| #24909707 | 2 |
| #358×D83 | 2 |
| #346×D83 | 2 |
| C83×#2245 | 2 |
| C2×#2245 | 83 |