Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14582722 | C2 | semidirect |
| 5. #19135348 | C2 | semidirect |
| 6. #19132701 | C2 | semidirect |
| 7. C43×#1375 | C2 | semidirect |
| 19. #14582701 | C4 | semidirect |
| 40. #13063259 | C2×C4 | semidirect |
| 54. C2×C16×C43 | C2×C4 | semidirect |
| 146. #1375 | D43 | semidirect |
| 168. C43 | #12956 | semidirect |
| 191. C2×C16 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583012 | 2 |
| C2×#14582722 | 2 |
| C2×#14582713 | 2 |
| #19136312 | 2 |
| #19135348 | 2 |
| #19132701 | 2 |
| C43×#1375 | 2 |
| #12956 | 43 |