Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
230 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊(C43⋊C32) | C2 | semidirect |
| 4. Dic43⋊C32 | C2 | semidirect |
| 5. C43×C4⋊C32 | C2 | semidirect |
| 59. C4×D43 | C32 | semidirect |
| 73. C4×C43 | C2×C32 | semidirect |
| 78. Dic43 | C2×C32 | semidirect |
| 83. C4⋊C32 | D43 | direct (N × H) |
| 87. D43 | C4⋊C32 | direct (N × H) |
| 98. C43 | C2×C4⋊C32 | semidirect |
| 158. C4 | C32×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D43 | 2 |
| C4×C16×D43 | 2 |
| C4⋊(C43⋊C32) | 2 |
| Dic43⋊C32 | 2 |
| C43×C4⋊C32 | 2 |
| C2×C4⋊C32 | 43 |