Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
814 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 3. #24909715 | C2 | direct (N × H) |
| 81. C2×C4×C83 | Q32 | semidirect |
| 100. C4×C83 | C2×Q32 | semidirect |
| 105. C2×C83 | #2247 | semidirect |
| 113. C83 | C2×#2247 | semidirect |
| 194. C2×C4 | #14581738 | semidirect |
| 209. C4 | C2×#14581738 | semidirect |
| 212. C2 | #24909715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581738 | 2 |
| C2×#19128081 | 2 |
| #24909715 | 2 |
| C2×C4×C83⋊C16 | 2 |
| C2×#494×C83 | 2 |
| C2×#2247 | 83 |