Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
252 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 117 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. D4×C83⋊C16 | C2 | semidirect |
| 2. #24905527 | C2 | semidirect |
| 3. D4⋊(C83⋊C16) | C2 | semidirect |
| 4. #24905381 | C2 | semidirect |
| 35. D8×C83 | C16 | semidirect |
| 49. D4×C83 | C2×C16 | semidirect |
| 60. C8×C83 | C2×C16 | semidirect |
| 82. C83 | #12062 | semidirect |
| 109. D8 | C83⋊C16 | semidirect |
| 126. D4 | C2×C83⋊C16 | semidirect |
| 137. C8 | C2×C83⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C83⋊C16 | 2 |
| #24905527 | 2 |
| D4⋊(C83⋊C16) | 2 |
| #24905381 | 2 |
| C8×D8×C83 | 2 |
| #12062 | 83 |