Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 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. #24909689 | C2 | semidirect |
| 9. C83×#2245 | C2 | semidirect |
| 151. #2245 | D83 | semidirect |
| 155. C83 | #33705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917976 | 2 |
| #494×D83 | 2 |
| #24909710 | 2 |
| #24909709 | 2 |
| #24909708 | 2 |
| #24909689 | 2 |
| #24909181 | 2 |
| #24909056 | 2 |
| C83×#2245 | 2 |
| #33705 | 83 |