Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #19132653 | C2 | semidirect |
| 5. Q8⋊(C43⋊C16) | C2 | semidirect |
| 6. #19132559 | C2 | semidirect |
| 7. Q8×Q16×C43 | C2 | semidirect |
| 61. Q16×C43 | SD16 | semidirect |
| 90. Q8×C43 | SD32 | semidirect |
| 124. Q8×Q16 | D43 | semidirect |
| 152. C43 | #12354 | semidirect |
| 189. Q16 | #10621884 | semidirect |
| 218. Q8 | #13063268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136820 | 2 |
| #19136635 | 2 |
| #19133955 | 2 |
| #19132653 | 2 |
| Q8⋊(C43⋊C16) | 2 |
| #19132559 | 2 |
| Q8×Q16×C43 | 2 |
| #12354 | 43 |