Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 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×D172 | C2 | semidirect |
| 3. #19132664 | C2 | semidirect |
| 4. D4⋊(C43⋊C16) | C2 | semidirect |
| 5. #19132549 | C2 | semidirect |
| 6. C16×C43⋊C8 | C2 | semidirect |
| 7. D4×C16×C43 | C2 | semidirect |
| 57. #10621882 | C16 | direct (N × H) |
| 68. C16×C43 | D8 | semidirect |
| 74. D4×C43 | C2×C16 | semidirect |
| 83. D172 | C2×C16 | semidirect |
| 93. C43⋊C8 | C2×C16 | semidirect |
| 110. D4×C16 | D43 | semidirect |
| 136. C43 | C16×D8 | semidirect |
| 184. C16 | #10621882 | direct (N × H) |
| 190. D4 | C16×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D172 | 2 |
| C8×#10621882 | 2 |
| #19132664 | 2 |
| D4⋊(C43⋊C16) | 2 |
| #19132549 | 2 |
| C16×C43⋊C8 | 2 |
| D4×C16×C43 | 2 |
| C16×D8 | 43 |