Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #19133414 | C2 | semidirect |
| 4. #19132660 | C2 | semidirect |
| 6. #19132517 | C2 | semidirect |
| 7. C43×#1334 | C2 | semidirect |
| 26. #13063268 | C8 | semidirect |
| 48. Q16×C43 | C2×C8 | semidirect |
| 66. C43⋊C16 | C2×C8 | semidirect |
| 103. #1334 | D43 | semidirect |
| 125. C43 | #12065 | semidirect |
| 151. Q16 | C8×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136457 | 2 |
| #19133418 | 2 |
| #19133414 | 2 |
| #19132660 | 2 |
| #19132563 | 2 |
| #19132517 | 2 |
| C43×#1334 | 2 |
| #12065 | 43 |