Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #24920419 | C2 | semidirect |
| 2. #24909704 | C2 | semidirect |
| 3. #24906944 | C2 | semidirect |
| 4. #24905514 | C2 | semidirect |
| 5. #24905444 | C2 | semidirect |
| 6. #24905430 | C2 | semidirect |
| 90. D8×C83 | SD16 | semidirect |
| 153. C83 | #12360 | semidirect |
| 221. D8 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920419 | 2 |
| #24909704 | 2 |
| #24906944 | 2 |
| #24905514 | 2 |
| #24905444 | 2 |
| #24905430 | 2 |
| C83×#2206 | 2 |
| #12360 | 83 |