Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1190 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. C2×#14582701 | C2 | semidirect |
| 3. #19134624 | C2 | semidirect |
| 4. C2×C43×C22⋊C16 | C2 | semidirect |
| 9. C22×D344 | C4 | semidirect |
| 11. C2×#13063259 | C22 | semidirect |
| 16. C22×C16×C43 | C22 | semidirect |
| 81. D344 | C22⋊C4 | semidirect |
| 123. C22×C43 | #357 | semidirect |
| 142. C2×C22⋊C16 | D43 | semidirect |
| 158. C22×C16 | C2×D43 | semidirect |
| 164. C43 | #12731 | semidirect |
| 275. C22 | #14582701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D344 | 2 |
| C2×#14582701 | 2 |
| #19134624 | 2 |
| C2×C43×C22⋊C16 | 2 |
| #12731 | 43 |