Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 93 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×C43⋊C16 | C2 | semidirect |
| 2. #19136414 | C2 | semidirect |
| 4. #19132658 | C2 | semidirect |
| 5. #19132551 | C2 | semidirect |
| 6. #19132514 | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 57. #10621882 | C16 | semidirect |
| 74. D4×C43 | C2×C16 | semidirect |
| 83. D172 | C2×C16 | semidirect |
| 93. C43⋊C8 | C2×C16 | semidirect |
| 114. D4⋊C16 | D43 | semidirect |
| 136. C43 | #12062 | semidirect |
| 190. D4 | C16×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C43⋊C16 | 2 |
| #19136414 | 2 |
| C8×#10621882 | 2 |
| #19132658 | 2 |
| #19132551 | 2 |
| #19132514 | 2 |
| C43×D4⋊C16 | 2 |
| #12062 | 43 |