Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
878 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 283 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. #24907079 | C2 | direct (N × H) |
| 47. C2×C83⋊C8 | Q16 | semidirect |
| 81. C83⋊C8 | C2×Q16 | semidirect |
| 92. C2×C83 | #1713 | semidirect |
| 100. C83 | C2×#1713 | semidirect |
| 186. C2 | #24907079 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128104 | 2 |
| C2×#19128081 | 2 |
| #24907079 | 2 |
| C2×C8×C83⋊C8 | 2 |
| C2×#494×C83 | 2 |
| C2×#1713 | 83 |