Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 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. #24908277 | C2 | semidirect |
| 3. #24907629 | C2 | semidirect |
| 4. C2×#19127441 | C2 | semidirect |
| 5. C2×#19127440 | C2 | semidirect |
| 6. #24905345 | C2 | semidirect |
| 7. C83×#1959 | C2 | semidirect |
| 54. #14581703 | D4 | semidirect |
| 240. #1959 | D83 | semidirect |
| 245. C83 | #10424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915508 | 2 |
| #24908277 | 2 |
| #24907629 | 2 |
| C2×#19127441 | 2 |
| C2×#19127440 | 2 |
| #24905345 | 2 |
| C83×#1959 | 2 |
| #10424 | 83 |