Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #19147733 | C2 | semidirect |
| 2. C2×#14582734 | C2 | semidirect |
| 3. #19136712 | C2 | semidirect |
| 4. #19132786 | C2 | semidirect |
| 5. #19132779 | C2 | semidirect |
| 6. #19132738 | C2 | semidirect |
| 7. C43×#2263 | C2 | semidirect |
| 17. C2×C43⋊C32 | C22 | semidirect |
| 18. #14582729 | C22 | semidirect |
| 21. C2×D16×C43 | C22 | semidirect |
| 24. C43×M64 | C22 | semidirect |
| 117. #2263 | D43 | semidirect |
| 136. C2×D16 | C2×D43 | semidirect |
| 142. M64 | C2×D43 | semidirect |
| 146. C43 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147733 | 2 |
| C2×#14582734 | 2 |
| #19136712 | 2 |
| #19132786 | 2 |
| #19132779 | 2 |
| #19132738 | 2 |
| C43×#2263 | 2 |
| #13669 | 43 |