Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
420 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 420 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. #24907478 | C2 | semidirect |
| 3. #24906238 | C2 | semidirect |
| 6. #24905322 | C2 | semidirect |
| 7. C83×#1461 | C2 | semidirect |
| 187. #1461 | 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 |
|---|---|
| #24916935 | 2 |
| #24907478 | 2 |
| #24906238 | 2 |
| #24906110 | 2 |
| #24906024 | 2 |
| #24905322 | 2 |
| C83×#1461 | 2 |
| #10466 | 83 |