Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C2×C32×D83 | C2 | semidirect |
| 3. Dic83⋊C32 | C2 | semidirect |
| 4. C22⋊(C83⋊C32) | C2 | semidirect |
| 5. (C2×D83)⋊C32 | C2 | semidirect |
| 6. C32×Dic83 | C2 | semidirect |
| 7. C22×C32×C83 | C2 | semidirect |
| 39. C32×C83 | D4 | semidirect |
| 66. C22⋊D83 | C32 | direct (N × H) |
| 79. C22×C83 | C2×C32 | semidirect |
| 83. C2×D83 | C2×C32 | semidirect |
| 89. Dic83 | C2×C32 | semidirect |
| 97. C22×C32 | D83 | semidirect |
| 103. C83 | D4×C32 | semidirect |
| 135. C32 | C22⋊D83 | direct (N × H) |
| 178. C22 | C32×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D83 | 2 |
| C16×C22⋊D83 | 2 |
| Dic83⋊C32 | 2 |
| C22⋊(C83⋊C32) | 2 |
| (C2×D83)⋊C32 | 2 |
| C32×Dic83 | 2 |
| C22×C32×C83 | 2 |
| D4×C32 | 83 |