Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
386 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24908239 | C2 | semidirect |
| 3. #24906143 | C2 | semidirect |
| 5. C2×#19127446 | C2 | semidirect |
| 6. #24905312 | C2 | semidirect |
| 180. C83 | #10552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917856 | 2 |
| #24908239 | 2 |
| #24906143 | 2 |
| #24906140 | 2 |
| C2×#19127446 | 2 |
| #24905312 | 2 |
| C83×#1480 | 2 |
| #10552 | 83 |