Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
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. #21448473 | C2 | semidirect |
| 3. #21446227 | C2 | semidirect |
| 4. #21446100 | C2 | semidirect |
| 5. #21445767 | C2 | semidirect |
| 6. C4×#14519692 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C61 | C2 | semidirect |
| 9. C22×#11758198 | C22 | semidirect |
| 10. #16839949 | C4 | semidirect |
| 18. #16839634 | C22 | semidirect |
| 19. #16839617 | C22 | semidirect |
| 20. C4×C22⋊Dic61 | C22 | semidirect |
| 21. #16839529 | C22 | semidirect |
| 33. #14519745 | C2×C4 | semidirect |
| 45. #14519692 | C2×C4 | semidirect |
| 55. C23×C4×C61 | D4 | semidirect |
| 69. C2×C4⋊C4×C61 | D4 | semidirect |
| 72. C2×C22⋊C4×C61 | D4 | semidirect |
| 75. C2×C42×C61 | D4 | semidirect |
| 83. C23×D61 | C22×C4 | semidirect |
| 126. C22⋊Dic61 | C22×C4 | semidirect |
| 215. C4×H(5,𝔽2) | D61 | semidirect |
| 250. C61 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D61 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D61 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D61 | semidirect |
| 292. C2×C42 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839949 | 2 |
| #21448473 | 2 |
| #21446227 | 2 |
| #21446100 | 2 |
| #21445767 | 2 |
| C4×#14519692 | 2 |
| C4×H(5,𝔽2)×C61 | 2 |
| #21482 | 61 |