Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24909321 | C2 | semidirect |
| 4. #24905662 | C2 | semidirect |
| 5. #24905645 | C2 | semidirect |
| 6. #24905596 | C2 | semidirect |
| 11. #19127539 | C4 | semidirect |
| 24. Dic664 | C2×C4 | semidirect |
| 30. C83⋊C32 | C2×C4 | semidirect |
| 93. C83 | #13652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127539 | 2 |
| #24909321 | 2 |
| D16×Dic83 | 2 |
| #24905662 | 2 |
| #24905645 | 2 |
| #24905596 | 2 |
| C83×#1415 | 2 |
| #13652 | 83 |