Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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. C22×C43⋊C32 | C2 | semidirect |
| 3. #19136681 | C2 | semidirect |
| 4. #19132794 | C2 | semidirect |
| 5. #19132773 | C2 | semidirect |
| 6. #19132772 | C2 | semidirect |
| 7. C43×#2215 | C2 | semidirect |
| 28. C43⋊C32 | D4 | semidirect |
| 84. C22×C43 | D32 | semidirect |
| 97. #2215 | D43 | semidirect |
| 120. C43 | #13694 | semidirect |
| 186. C22 | #14582734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582734 | 2 |
| C22×C43⋊C32 | 2 |
| #19136681 | 2 |
| #19132794 | 2 |
| #19132773 | 2 |
| #19132772 | 2 |
| C43×#2215 | 2 |
| #13694 | 43 |