Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14582738 | C2 | semidirect |
| 2. C2×#14582737 | C2 | semidirect |
| 3. C2×#14582734 | C2 | semidirect |
| 4. #19136853 | C2 | semidirect |
| 5. #19136843 | C2 | semidirect |
| 6. #19132728 | C2 | semidirect |
| 7. C2×C43×D32 | C2 | semidirect |
| 37. C43⋊C32 | D4 | semidirect |
| 45. C32×C43 | D4 | semidirect |
| 101. C2×D32 | D43 | semidirect |
| 125. C43 | #13729 | semidirect |
| 148. C32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582738 | 2 |
| C2×#14582737 | 2 |
| C2×#14582734 | 2 |
| #19136853 | 2 |
| #19136843 | 2 |
| #19132728 | 2 |
| C2×C43×D32 | 2 |
| #13729 | 43 |