Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
322 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #24909680 | C2 | semidirect |
| 2. #24909675 | C2 | semidirect |
| 3. #24909016 | C2 | semidirect |
| 4. #24905451 | C2 | semidirect |
| 5. #24905448 | C2 | semidirect |
| 6. #24905401 | C2 | semidirect |
| 161. C83 | #12303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909680 | 2 |
| #24909675 | 2 |
| #24909016 | 2 |
| #24905451 | 2 |
| #24905448 | 2 |
| #24905401 | 2 |
| C83×#3204 | 2 |
| #12303 | 83 |