Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
782 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 320 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×#16840689 | C2 | direct (N × H) |
| 7. #16840689 | C22 | direct (N × H) |
| 9. C22×#11758185 | C4 | semidirect |
| 10. C2×C16×D61 | C4 | semidirect |
| 12. C22×C16×C61 | C4 | semidirect |
| 24. C2×#11758185 | C2×C4 | semidirect |
| 25. C16×D61 | C2×C4 | semidirect |
| 28. C2×C16×C61 | C2×C4 | semidirect |
| 49. C16×C61 | C22×C4 | semidirect |
| 50. #11758185 | C22×C4 | semidirect |
| 71. C22×C61 | #367 | semidirect |
| 73. C2×D61 | #367 | semidirect |
| 85. C2×C61 | C2×#367 | semidirect |
| 87. D61 | C2×#367 | semidirect |
| 94. C22×C16 | #6923 | semidirect |
| 98. C61 | C22×#367 | semidirect |
| 112. C2×C16 | C2×#6923 | semidirect |
| 136. C16 | C22×#6923 | semidirect |
| 160. C22 | #16840689 | direct (N × H) |
| 169. C2 | C2×#16840689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519846 | 2 |
| C2×#16840689 | 2 |
| C22×C16×D61 | 2 |
| C22×#367 | 61 |