Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1630 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 283 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. #19137249 | C2 | semidirect |
| 3. #19135003 | C2 | semidirect |
| 4. #19134876 | C2 | semidirect |
| 5. #19134543 | C2 | semidirect |
| 6. C4×#13063240 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C43 | C2 | semidirect |
| 9. C22×(C2×D43)⋊C4 | C22 | semidirect |
| 10. #14583086 | C4 | semidirect |
| 18. #14582771 | C22 | semidirect |
| 19. #14582754 | C22 | semidirect |
| 20. C4×C22⋊Dic43 | C22 | semidirect |
| 21. #14582666 | C22 | semidirect |
| 33. #13063293 | C2×C4 | semidirect |
| 45. #13063240 | C2×C4 | semidirect |
| 55. C23×C4×C43 | D4 | semidirect |
| 69. C2×C4⋊C4×C43 | D4 | semidirect |
| 72. C2×C22⋊C4×C43 | D4 | semidirect |
| 75. C2×C42×C43 | D4 | semidirect |
| 83. C23×D43 | C22×C4 | semidirect |
| 126. C22⋊Dic43 | C22×C4 | semidirect |
| 215. C4×H(5,𝔽2) | D43 | semidirect |
| 250. C43 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D43 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D43 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D43 | semidirect |
| 292. C2×C42 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583086 | 2 |
| #19137249 | 2 |
| #19135003 | 2 |
| #19134876 | 2 |
| #19134543 | 2 |
| C4×#13063240 | 2 |
| C4×H(5,𝔽2)×C43 | 2 |
| #21482 | 43 |