Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
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×D43 | C2 | semidirect |
| 3. C4⋊(C43⋊C32) | C2 | semidirect |
| 4. (C2×D43)⋊C32 | C2 | semidirect |
| 5. C4×C32×C43 | C2 | semidirect |
| 27. C32×C43 | D4 | semidirect |
| 47. D172 | C32 | direct (N × H) |
| 58. C2×D43 | C2×C32 | semidirect |
| 60. C4×C43 | C2×C32 | semidirect |
| 68. C4×C32 | D43 | semidirect |
| 82. C43 | D4×C32 | semidirect |
| 95. C32 | D172 | direct (N × H) |
| 128. 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 |
| C16×D172 | 2 |
| C4⋊(C43⋊C32) | 2 |
| (C2×D43)⋊C32 | 2 |
| C4×C32×C43 | 2 |
| D4×C32 | 43 |