Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 2. C2×#14583186 | C2 | semidirect |
| 3. #19133738 | C2 | direct (N × H) |
| 4. C2×#14582648 | C2 | semidirect |
| 5. C2×#14582628 | C2 | semidirect |
| 6. C2×C43×#494 | C2 | semidirect |
| 15. #14583186 | C22 | semidirect |
| 19. #14582648 | C22 | semidirect |
| 20. #14582628 | C22 | semidirect |
| 25. C43×#494 | C22 | semidirect |
| 153. C2×#494 | D43 | semidirect |
| 158. C2×C43 | #1634 | semidirect |
| 173. #494 | C2×D43 | semidirect |
| 182. C43 | C2×#1634 | semidirect |
| 308. C2 | #19133738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583615 | 2 |
| C2×#14583186 | 2 |
| #19133738 | 2 |
| C2×#14582648 | 2 |
| C2×#14582628 | 2 |
| C2×C43×#494 | 2 |
| C2×#1634 | 43 |