Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#16840196 | C2 | semidirect |
| 2. #21456246 | C2 | semidirect |
| 3. #493×D61 | C2 | semidirect |
| 4. #21448082 | C2 | semidirect |
| 5. #21448075 | C2 | semidirect |
| 6. #21448074 | C2 | semidirect |
| 7. #21448068 | C2 | semidirect |
| 8. C4×#14519716 | C2 | semidirect |
| 9. C61×#2246 | C2 | semidirect |
| 17. C2×#14519722 | C22 | semidirect |
| 18. C2×#14519721 | C22 | semidirect |
| 19. C2×#14519718 | C22 | semidirect |
| 22. #16840145 | C22 | semidirect |
| 23. #16840142 | C22 | semidirect |
| 30. #16839537 | C22 | semidirect |
| 31. C4×#11758185 | C22 | semidirect |
| 32. C2×D16×C61 | C22 | semidirect |
| 34. C61×#493 | C22 | semidirect |
| 35. C4×C16×C61 | C22 | semidirect |
| 64. #14519716 | D4 | semidirect |
| 120. C16×C61 | C2×D4 | semidirect |
| 121. #11758185 | C2×D4 | semidirect |
| 166. C4×C61 | #509 | semidirect |
| 179. #2246 | D61 | semidirect |
| 197. C2×D16 | C2×D61 | semidirect |
| 207. #493 | C2×D61 | semidirect |
| 212. C4×C16 | C2×D61 | semidirect |
| 213. C61 | #33717 | semidirect |
| 299. C16 | D4×D61 | semidirect |
| 346. C4 | #16840196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840196 | 2 |
| #21456246 | 2 |
| #493×D61 | 2 |
| #21448082 | 2 |
| #21448075 | 2 |
| #21448074 | 2 |
| #21448068 | 2 |
| C4×#14519716 | 2 |
| C61×#2246 | 2 |
| #33717 | 61 |