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. #24907588 | C2 | semidirect |
| 4. #24905565 | C2 | semidirect |
| 5. #24905560 | C2 | semidirect |
| 6. #24905553 | 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 |
|---|---|
| #24909170 | 2 |
| #24908362 | 2 |
| #24907588 | 2 |
| #24905565 | 2 |
| #24905560 | 2 |
| #24905553 | 2 |
| C83×#2148 | 2 |
| #13489 | 83 |