Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #24905443 | C2 | semidirect |
| 5. Q8⋊(C83⋊C16) | C2 | semidirect |
| 6. #24905441 | C2 | semidirect |
| 7. C83×Q8⋊C16 | C2 | semidirect |
| 152. Q8⋊C16 | D83 | semidirect |
| 153. C83 | #11640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916392 | 2 |
| #24909265 | 2 |
| #24909260 | 2 |
| #24905443 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905441 | 2 |
| C83×Q8⋊C16 | 2 |
| #11640 | 83 |