Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
312 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 75 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. #19136820 | C2 | semidirect |
| 3. #19133955 | C2 | semidirect |
| 4. #19132653 | C2 | semidirect |
| 5. Q8⋊(C43⋊C16) | C2 | semidirect |
| 6. #19132556 | C2 | semidirect |
| 7. C43×#3380 | C2 | semidirect |
| 62. D8×C43 | SD16 | semidirect |
| 128. #3380 | D43 | semidirect |
| 157. C43 | #12355 | semidirect |
| 199. D8 | #10621884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136820 | 2 |
| #19136630 | 2 |
| #19133955 | 2 |
| #19132653 | 2 |
| Q8⋊(C43⋊C16) | 2 |
| #19132556 | 2 |
| C43×#3380 | 2 |
| #12355 | 43 |