Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24907626 | C2 | semidirect |
| 4. #24905572 | C2 | semidirect |
| 5. #24905571 | C2 | semidirect |
| 6. #24905544 | C2 | semidirect |
| 153. C83 | #13485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909175 | 2 |
| #24908352 | 2 |
| #24907626 | 2 |
| #24905572 | 2 |
| #24905571 | 2 |
| #24905544 | 2 |
| C83×#2139 | 2 |
| #13485 | 83 |