Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#19127539 | C2 | semidirect |
| 2. #24909721 | C2 | semidirect |
| 3. D16×Dic83 | C2 | semidirect |
| 4. Dic83⋊C32 | C2 | semidirect |
| 5. #24905645 | C2 | semidirect |
| 6. #24905641 | C2 | semidirect |
| 105. C83 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127539 | 2 |
| #24909721 | 2 |
| D16×Dic83 | 2 |
| Dic83⋊C32 | 2 |
| #24905645 | 2 |
| #24905641 | 2 |
| C2×D32×C83 | 2 |
| #13689 | 83 |