Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
298 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 298 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×#14583331 | C2 | semidirect |
| 2. C2×#14582737 | C2 | semidirect |
| 3. C2×#14582734 | C2 | semidirect |
| 4. #19132775 | C2 | semidirect |
| 5. #19132772 | C2 | semidirect |
| 6. C22⋊(C43⋊C32) | C2 | semidirect |
| 7. C43×#2215 | C2 | semidirect |
| 30. Dic344 | D4 | semidirect |
| 33. D688 | D4 | semidirect |
| 112. #2215 | D43 | semidirect |
| 137. C43 | #13663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583331 | 2 |
| C2×#14582737 | 2 |
| C2×#14582734 | 2 |
| #19132775 | 2 |
| #19132772 | 2 |
| C22⋊(C43⋊C32) | 2 |
| C43×#2215 | 2 |
| #13663 | 43 |