Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
218 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
| 4. #24905532 | C2 | semidirect |
| 6. #24905382 | C2 | semidirect |
| 7. C83×Q8⋊C16 | C2 | semidirect |
| 88. C83⋊C8 | M32 | semidirect |
| 110. Q8⋊C16 | D83 | semidirect |
| 113. C83 | #12058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909372 | 2 |
| #24909294 | 2 |
| C8×#13050577 | 2 |
| #24905532 | 2 |
| #24905419 | 2 |
| #24905382 | 2 |
| C83×Q8⋊C16 | 2 |
| #12058 | 83 |