Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14582734 | C2 | semidirect |
| 2. C2×C32×D43 | C2 | semidirect |
| 3. #19136682 | C2 | semidirect |
| 4. #19136678 | C2 | semidirect |
| 5. #19132794 | C2 | semidirect |
| 6. #19132774 | C2 | semidirect |
| 7. C43×#1415 | C2 | semidirect |
| 33. C43⋊C32 | D4 | semidirect |
| 88. C2×D43 | D32 | semidirect |
| 100. #1415 | D43 | semidirect |
| 120. C43 | #13694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582734 | 2 |
| C2×C32×D43 | 2 |
| #19136682 | 2 |
| #19136678 | 2 |
| #19132794 | 2 |
| #19132774 | 2 |
| C43×#1415 | 2 |
| #13694 | 43 |