Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
550 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19127908 | C2 | semidirect |
| 3. #24906135 | C2 | semidirect |
| 5. #24905786 | C2 | semidirect |
| 6. #24905359 | C2 | semidirect |
| 215. C83 | #10185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916931 | 2 |
| C2×#19127908 | 2 |
| #24906135 | 2 |
| #24905862 | 2 |
| #24905786 | 2 |
| #24905359 | 2 |
| C83×#3226 | 2 |
| #10185 | 83 |