Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
514 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 147 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×C4⋊(C83⋊C16) | C2 | semidirect |
| 3. C2×#19127504 | C2 | semidirect |
| 5. C4×#107×C83 | C2 | semidirect |
| 12. #19128085 | C4 | semidirect |
| 142. C4×#107 | D83 | semidirect |
| 143. C83 | #13254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128085 | 2 |
| C2×C4⋊(C83⋊C16) | 2 |
| C2×#19127504 | 2 |
| C2×#19127501 | 2 |
| C4×#107×C83 | 2 |
| #13254 | 83 |