Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
460 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24908432 | C2 | semidirect |
| 4. #24907631 | C2 | semidirect |
| 5. C2×#19127442 | C2 | semidirect |
| 6. #24905345 | C2 | semidirect |
| 217. C83 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915514 | 2 |
| #24908432 | 2 |
| #24908280 | 2 |
| #24907631 | 2 |
| C2×#19127442 | 2 |
| #24905345 | 2 |
| C2×#329×C83 | 2 |
| #10427 | 83 |