Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1502 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 240 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. C2×#16840668 | C2 | direct (N × H) |
| 7. #16840668 | C22 | direct (N × H) |
| 10. C2×#14519766 | C4 | semidirect |
| 13. C22×C4×Dic61 | C4 | semidirect |
| 14. C23×Q8×C61 | C4 | semidirect |
| 29. #14519766 | C2×C4 | semidirect |
| 34. C2×C4×Dic61 | C2×C4 | semidirect |
| 38. C22×Q8×C61 | C2×C4 | semidirect |
| 54. C2×Q8×C61 | C22×C4 | semidirect |
| 79. C4×Dic61 | C22×C4 | semidirect |
| 116. C22×C61 | #354 | semidirect |
| 138. C2×C61 | C2×#354 | semidirect |
| 142. C23×Q8 | #6923 | semidirect |
| 153. C61 | C22×#354 | semidirect |
| 158. C22×Q8 | C2×#6923 | semidirect |
| 191. C2×Q8 | C22×#6923 | semidirect |
| 262. C22 | #16840668 | direct (N × H) |
| 275. C2 | C2×#16840668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519836 | 2 |
| C2×#16840668 | 2 |
| C22×#14519766 | 2 |
| C22×#354 | 61 |