Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×D1328 | C2 | semidirect |
| 3. #24905662 | C2 | semidirect |
| 4. #24905641 | C2 | semidirect |
| 5. #24905640 | C2 | semidirect |
| 6. C4×C83⋊C32 | C2 | semidirect |
| 7. C4×D16×C83 | C2 | semidirect |
| 10. #19127536 | C4 | direct (N × H) |
| 23. D1328 | C2×C4 | semidirect |
| 27. C83⋊C32 | C2×C4 | semidirect |
| 31. D16×C83 | C2×C4 | semidirect |
| 80. C4×C83 | D32 | semidirect |
| 92. C4×D16 | D83 | semidirect |
| 97. C83 | C4×D32 | semidirect |
| 117. D16 | C4×D83 | semidirect |
| 171. C4 | #19127536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127536 | 2 |
| C4×D1328 | 2 |
| #24905662 | 2 |
| #24905641 | 2 |
| #24905640 | 2 |
| C4×C83⋊C32 | 2 |
| C4×D16×C83 | 2 |
| C4×D32 | 83 |