Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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×C22⋊(C43⋊C16) | C2 | semidirect |
| 3. #19132609 | C2 | direct (N × H) |
| 4. C2×C43×#341 | C2 | semidirect |
| 15. C22⋊(C43⋊C16) | C22 | semidirect |
| 19. C43×#341 | C22 | semidirect |
| 149. C2×#341 | D43 | semidirect |
| 153. C2×C43 | #1349 | semidirect |
| 172. #341 | C2×D43 | semidirect |
| 173. C43 | C2×#1349 | semidirect |
| 303. C2 | #19132609 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583135 | 2 |
| C2×C22⋊(C43⋊C16) | 2 |
| #19132609 | 2 |
| C2×C43×#341 | 2 |
| C2×#1349 | 43 |