Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
586 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 586 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 |
|---|---|---|
| 1. C22×#13063266 | C2 | semidirect |
| 2. #19145082 | C2 | semidirect |
| 3. C2×#14582713 | C2 | semidirect |
| 4. C2×#14582706 | C2 | semidirect |
| 5. #19135506 | C2 | semidirect |
| 6. #19132685 | C2 | semidirect |
| 7. C2×C43×#509 | C2 | semidirect |
| 52. C2×C43⋊C16 | D4 | semidirect |
| 73. C2×D8×C43 | D4 | semidirect |
| 78. M32×C43 | D4 | semidirect |
| 200. C2×#509 | D43 | semidirect |
| 237. C43 | #13336 | semidirect |
| 263. C2×D8 | C22⋊D43 | semidirect |
| 276. M32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13063266 | 2 |
| #19145082 | 2 |
| C2×#14582713 | 2 |
| C2×#14582706 | 2 |
| #19135506 | 2 |
| #19132685 | 2 |
| C2×C43×#509 | 2 |
| #13336 | 43 |