Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
218 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24909372 | C2 | semidirect |
| 3. #24905533 | C2 | semidirect |
| 4. Q8⋊(C83⋊C16) | C2 | semidirect |
| 6. #24905381 | C2 | semidirect |
| 86. C8×C83 | M32 | semidirect |
| 113. C83 | #12058 | semidirect |
| 192. C8 | #14581732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909372 | 2 |
| #24909295 | 2 |
| #24905533 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| D4⋊(C83⋊C16) | 2 |
| #24905381 | 2 |
| C8×SD16×C83 | 2 |
| #12058 | 83 |