Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
702 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 280 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×#16840686 | C2 | direct (N × H) |
| 11. #16840686 | C22 | direct (N × H) |
| 13. C2×#14519716 | C4 | semidirect |
| 15. C22×#11758185 | C4 | semidirect |
| 16. C22×C16×C61 | C4 | semidirect |
| 33. #14519716 | C2×C4 | semidirect |
| 35. C2×#11758185 | C2×C4 | semidirect |
| 37. C2×C16×C61 | C2×C4 | semidirect |
| 61. C16×C61 | C22×C4 | semidirect |
| 62. #11758185 | C22×C4 | semidirect |
| 84. C22×C61 | #365 | semidirect |
| 99. C2×C61 | C2×#365 | semidirect |
| 109. C22×C16 | #6923 | semidirect |
| 115. C61 | C22×#365 | semidirect |
| 132. C2×C16 | C2×#6923 | semidirect |
| 161. C16 | C22×#6923 | semidirect |
| 186. C22 | #16840686 | direct (N × H) |
| 195. C2 | C2×#16840686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519847 | 2 |
| C22×#14519845 | 2 |
| C2×#16840686 | 2 |
| C22×#14519716 | 2 |
| C22×#365 | 61 |