Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#14583332 | C2 | semidirect |
| 2. C2×#14583328 | C2 | semidirect |
| 3. #19136903 | C2 | direct (N × H) |
| 4. C2×#14582739 | C2 | semidirect |
| 5. C2×#14582738 | C2 | semidirect |
| 6. C2×#14582734 | C2 | semidirect |
| 7. C2×C32×D43 | C2 | semidirect |
| 8. C2×C43×SD64 | C2 | semidirect |
| 12. #14583332 | C22 | semidirect |
| 14. #14583328 | C22 | semidirect |
| 20. #14582739 | C22 | semidirect |
| 21. #14582738 | C22 | semidirect |
| 22. #14582734 | C22 | semidirect |
| 24. C32×D43 | C22 | semidirect |
| 27. C43×SD64 | C22 | semidirect |
| 130. C2×SD64 | D43 | semidirect |
| 134. C2×C43 | #2262 | semidirect |
| 153. SD64 | C2×D43 | semidirect |
| 158. C43 | C2×#2262 | semidirect |
| 257. C2 | #19136903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583332 | 2 |
| C2×#14583328 | 2 |
| #19136903 | 2 |
| C2×#14582739 | 2 |
| C2×#14582738 | 2 |
| C2×#14582734 | 2 |
| C2×C32×D43 | 2 |
| C2×C43×SD64 | 2 |
| C2×#2262 | 43 |