Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21456557 | C2 | semidirect |
| 2. #21448033 | C2 | semidirect |
| 3. #21447990 | C2 | semidirect |
| 4. #21447895 | C2 | semidirect |
| 5. #21447765 | C2 | semidirect |
| 6. #21447717 | C2 | semidirect |
| 7. #21447631 | C2 | semidirect |
| 8. C61×#2956 | C2 | semidirect |
| 11. #16840160 | C22 | semidirect |
| 12. #16840139 | C22 | semidirect |
| 17. #16839875 | C22 | semidirect |
| 18. #16839586 | C22 | semidirect |
| 19. #16839583 | C22 | semidirect |
| 20. #16839574 | C22 | semidirect |
| 23. #16839540 | C22 | semidirect |
| 89. Q16×C61 | #41 | semidirect |
| 93. D8×C61 | #41 | semidirect |
| 166. #2956 | D61 | semidirect |
| 202. C61 | #33688 | semidirect |
| 259. Q16 | #11758222 | semidirect |
| 265. D8 | #11758222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456557 | 2 |
| #21448033 | 2 |
| #21447990 | 2 |
| #21447895 | 2 |
| #21447765 | 2 |
| #21447717 | 2 |
| #21447631 | 2 |
| C61×#2956 | 2 |
| #33688 | 61 |