Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 2. #24909001 | C2 | semidirect |
| 3. #24909000 | C2 | semidirect |
| 5. #24905288 | C2 | semidirect |
| 7. C83×#1272 | C2 | semidirect |
| 200. #1272 | D83 | semidirect |
| 202. C83 | #7833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915407 | 2 |
| #24909001 | 2 |
| #24909000 | 2 |
| #24908995 | 2 |
| #24905288 | 2 |
| #24905283 | 2 |
| C83×#1272 | 2 |
| #7833 | 83 |