Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24907586 | C2 | semidirect |
| 4. #24905564 | C2 | semidirect |
| 5. #24905559 | C2 | semidirect |
| 6. #24905551 | C2 | semidirect |
| 144. C83 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909212 | 2 |
| #24908362 | 2 |
| #24907586 | 2 |
| #24905564 | 2 |
| #24905559 | 2 |
| #24905551 | 2 |
| C83×#2138 | 2 |
| #13489 | 83 |