Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24906154 | C2 | semidirect |
| 5. #24905865 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#1950 | C2 | semidirect |
| 178. #1950 | D83 | semidirect |
| 184. C83 | #10553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917838 | 2 |
| #24906154 | 2 |
| #24906132 | 2 |
| C2×#19127444 | 2 |
| #24905865 | 2 |
| #24905314 | 2 |
| C83×#1950 | 2 |
| #10553 | 83 |