Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 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. C16×Dic86 | C2 | semidirect |
| 3. #19132658 | C2 | semidirect |
| 4. #19132573 | C2 | semidirect |
| 6. C16×C43⋊C8 | C2 | semidirect |
| 55. #10621883 | C16 | direct (N × H) |
| 65. C16×C43 | SD16 | semidirect |
| 80. Dic86 | C2×C16 | semidirect |
| 88. C43⋊C8 | C2×C16 | semidirect |
| 128. C43 | C16×SD16 | semidirect |
| 173. C16 | #10621883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic86 | 2 |
| C8×#10621883 | 2 |
| #19132658 | 2 |
| #19132573 | 2 |
| D4⋊(C43⋊C16) | 2 |
| C16×C43⋊C8 | 2 |
| D4×C16×C43 | 2 |
| C16×SD16 | 43 |