Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 314 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. #24909217 | C2 | semidirect |
| 3. #24906217 | C2 | semidirect |
| 4. #24905516 | C2 | semidirect |
| 5. #24905514 | C2 | semidirect |
| 6. #24905506 | C2 | semidirect |
| 7. C83×#1360 | C2 | semidirect |
| 157. #1360 | D83 | semidirect |
| 158. C83 | #11980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918030 | 2 |
| #24909217 | 2 |
| #24906217 | 2 |
| #24905516 | 2 |
| #24905514 | 2 |
| #24905506 | 2 |
| C83×#1360 | 2 |
| #11980 | 83 |