Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. C2×#16840649 | C2 | semidirect |
| 4. #108×#6923 | C2 | semidirect |
| 5. #21460882 | C2 | semidirect |
| 6. #21460881 | C2 | semidirect |
| 18. #16840677 | C4 | semidirect |
| 19. #16840676 | C4 | semidirect |
| 25. #16839570 | C4 | semidirect |
| 26. #16839569 | C4 | semidirect |
| 27. #16839568 | C4 | semidirect |
| 28. C61×#359 | C4 | semidirect |
| 39. D61⋊C16 | C2×C4 | semidirect |
| 41. #14519848 | C2×C4 | semidirect |
| 62. C2×#11758185 | C2×C4 | semidirect |
| 65. #14519713 | C2×C4 | semidirect |
| 68. C2×C16×C61 | C2×C4 | semidirect |
| 69. #108×C61 | C2×C4 | semidirect |
| 205. #359 | #6923 | semidirect |
| 208. C61 | #12640 | semidirect |
| 236. C2×C16 | C2×#6923 | semidirect |
| 241. #108 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#6923 | 2 |
| D61⋊#359 | 2 |
| C2×#16840649 | 2 |
| #108×#6923 | 2 |
| #21460882 | 2 |
| #21460881 | 2 |
| #359×D61 | 2 |
| #12640 | 61 |