Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
914 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 251 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×#14583302 | C2 | semidirect |
| 4. #19134267 | C2 | direct (N × H) |
| 5. C2×#14582620 | C2 | semidirect |
| 6. C2×C43×#494 | C2 | semidirect |
| 11. #14583302 | C22 | semidirect |
| 19. #14582620 | C22 | semidirect |
| 23. C43×#494 | C22 | semidirect |
| 125. C2×#494 | D43 | semidirect |
| 130. C2×C43 | #1722 | semidirect |
| 142. #494 | C2×D43 | semidirect |
| 152. C43 | C2×#1722 | semidirect |
| 252. C2 | #19134267 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583302 | 2 |
| C2×#14583272 | 2 |
| C2×#14583247 | 2 |
| #19134267 | 2 |
| C2×#14582620 | 2 |
| C2×C43×#494 | 2 |
| C2×#1722 | 43 |