Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
330 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24907616 | C2 | semidirect |
| 4. #24905360 | C2 | semidirect |
| 5. #24905359 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 162. C83 | #10627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908296 | 2 |
| #24907616 | 2 |
| #24906112 | 2 |
| #24905360 | 2 |
| #24905359 | 2 |
| #24905291 | 2 |
| C83×#1540 | 2 |
| #10627 | 83 |