Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19127525 | C2 | semidirect |
| 4. #24908251 | C2 | semidirect |
| 5. #24905562 | C2 | semidirect |
| 6. #24905550 | C2 | semidirect |
| 19. #19127508 | C4 | semidirect |
| 37. C2×C83⋊C16 | C2×C4 | semidirect |
| 39. #14581728 | C2×C4 | semidirect |
| 159. C83 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916347 | 2 |
| C2×#19127525 | 2 |
| #24909191 | 2 |
| #24908251 | 2 |
| #24905562 | 2 |
| #24905550 | 2 |
| C83×#2148 | 2 |
| #12949 | 83 |