Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19143396 | C2 | semidirect |
| 2. C2×#14582709 | C2 | semidirect |
| 3. #19136311 | C2 | semidirect |
| 4. #19135472 | C2 | semidirect |
| 5. #19132701 | C2 | semidirect |
| 6. #19132678 | C2 | semidirect |
| 24. C43×#509 | C4 | semidirect |
| 63. C2×D8×C43 | C2×C4 | semidirect |
| 69. M32×C43 | C2×C4 | semidirect |
| 91. Q16×C43 | C22⋊C4 | semidirect |
| 99. D8×C43 | C22⋊C4 | semidirect |
| 196. #509 | Dic43 | semidirect |
| 212. C43 | #13025 | semidirect |
| 226. C2×D8 | C2×Dic43 | semidirect |
| 244. M32 | C2×Dic43 | semidirect |
| 276. Q16 | C22⋊Dic43 | semidirect |
| 284. D8 | C22⋊Dic43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143396 | 2 |
| C2×#14582709 | 2 |
| #19136311 | 2 |
| #19135472 | 2 |
| #19132701 | 2 |
| #19132678 | 2 |
| C2×C43×#509 | 2 |
| #13025 | 43 |