Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 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. C22×#14581733 | C2 | semidirect |
| 2. C2×#19127971 | C2 | semidirect |
| 3. C2×#19127514 | C2 | semidirect |
| 4. #24909178 | C2 | semidirect |
| 5. C2×#19127485 | C2 | semidirect |
| 6. #24905558 | C2 | semidirect |
| 7. C83×#3058 | C2 | semidirect |
| 38. C2×D664 | D4 | semidirect |
| 47. C2×C83⋊C16 | D4 | semidirect |
| 49. #14581728 | D4 | semidirect |
| 202. #3058 | D83 | semidirect |
| 207. C83 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581733 | 2 |
| C2×#19127971 | 2 |
| C2×#19127514 | 2 |
| #24909178 | 2 |
| C2×#19127485 | 2 |
| #24905558 | 2 |
| C83×#3058 | 2 |
| #13319 | 83 |