Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 420 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. #24907475 | C2 | semidirect |
| 3. #24906239 | C2 | semidirect |
| 6. #24905786 | C2 | semidirect |
| 7. C83×#1286 | C2 | semidirect |
| 188. #1286 | D83 | semidirect |
| 189. C83 | #10466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916937 | 2 |
| #24907475 | 2 |
| #24906239 | 2 |
| #24906110 | 2 |
| #24906022 | 2 |
| #24905786 | 2 |
| C83×#1286 | 2 |
| #10466 | 83 |