Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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×D16×D61 | C2 | semidirect |
| 2. #493×D61 | C2 | semidirect |
| 3. #21448069 | C2 | semidirect |
| 4. #21448068 | C2 | semidirect |
| 5. #21448067 | C2 | semidirect |
| 6. C4×C16×D61 | C2 | semidirect |
| 7. C61×#2246 | C2 | semidirect |
| 11. C2×D976 | C22 | semidirect |
| 12. C2×#14519718 | C22 | semidirect |
| 15. #16840139 | C22 | semidirect |
| 18. #16840137 | C22 | semidirect |
| 20. C4×#11758185 | C22 | semidirect |
| 21. C16×Dic61 | C22 | semidirect |
| 22. C2×D16×C61 | C22 | semidirect |
| 23. C61×#493 | C22 | semidirect |
| 24. C4×C16×C61 | C22 | semidirect |
| 42. C16×D61 | D4 | semidirect |
| 79. C16×C61 | C2×D4 | semidirect |
| 80. #11758185 | C2×D4 | semidirect |
| 98. C4×D61 | D16 | semidirect |
| 114. C4×C61 | C2×D16 | semidirect |
| 118. Dic61 | C2×D16 | semidirect |
| 124. #2246 | D61 | direct (N × H) |
| 130. D61 | #2246 | direct (N × H) |
| 137. C2×D16 | C2×D61 | semidirect |
| 143. #493 | C2×D61 | semidirect |
| 147. C4×C16 | C2×D61 | semidirect |
| 148. C61 | C2×#2246 | semidirect |
| 204. C16 | D4×D61 | semidirect |
| 239. C4 | D16×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D61 | 2 |
| #493×D61 | 2 |
| #21448069 | 2 |
| #21448068 | 2 |
| #21448067 | 2 |
| C4×C16×D61 | 2 |
| C61×#2246 | 2 |
| C2×#2246 | 61 |