Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19127515 | C2 | semidirect |
| 3. #24909180 | C2 | semidirect |
| 4. #24907342 | C2 | semidirect |
| 5. C2×#364×C83 | C2 | semidirect |
| 10. #19128078 | C4 | semidirect |
| 37. #14581728 | D4 | semidirect |
| 38. #14581726 | D4 | semidirect |
| 133. C2×#364 | D83 | semidirect |
| 137. C83 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128078 | 2 |
| C2×#19127515 | 2 |
| #24909180 | 2 |
| #24907342 | 2 |
| C2×#364×C83 | 2 |
| #13261 | 83 |