Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 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. #24913339 | C2 | semidirect |
| 3. #24906089 | C2 | semidirect |
| 5. #24905910 | C2 | semidirect |
| 6. #24905329 | C2 | semidirect |
| 197. C83 | #10021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917863 | 2 |
| #24913339 | 2 |
| #24906089 | 2 |
| #24906010 | 2 |
| #24905910 | 2 |
| #24905329 | 2 |
| C83×#3112 | 2 |
| #10021 | 83 |