Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
392 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×C22⋊(C83⋊C16) | C2 | semidirect |
| 3. #24905404 | C2 | semidirect |
| 4. #24905388 | C2 | semidirect |
| 5. C83×#2112 | C2 | semidirect |
| 170. #2112 | D83 | semidirect |
| 174. C83 | #11470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916157 | 2 |
| C2×C22⋊(C83⋊C16) | 2 |
| #24905404 | 2 |
| #24905388 | 2 |
| C83×#2112 | 2 |
| #11470 | 83 |