Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #19136392 | C2 | semidirect |
| 3. #19136349 | C2 | semidirect |
| 4. #19132575 | C2 | semidirect |
| 5. #19132573 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 105. D4×C43 | M32 | semidirect |
| 126. Dic86 | M32 | semidirect |
| 159. D4⋊C16 | D43 | semidirect |
| 184. C43 | #11623 | semidirect |
| 266. D4 | #13063264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#10621900 | 2 |
| #19136392 | 2 |
| #19136349 | 2 |
| #19132575 | 2 |
| #19132573 | 2 |
| D4⋊(C43⋊C16) | 2 |
| C43×D4⋊C16 | 2 |
| #11623 | 43 |