Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #24907634 | C2 | semidirect |
| 3. #24906149 | C2 | semidirect |
| 4. #24906143 | C2 | semidirect |
| 6. #24905756 | C2 | semidirect |
| 157. C83 | #9774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128047 | 2 |
| #24907634 | 2 |
| #24906149 | 2 |
| #24906143 | 2 |
| #24906131 | 2 |
| #24905756 | 2 |
| C83×#1545 | 2 |
| #9774 | 83 |