Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1230 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 327 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×#16839839 | C2 | semidirect |
| 3. #21446612 | C2 | semidirect |
| 4. C42×#92418 | C2 | semidirect |
| 5. C61×#1842 | C2 | semidirect |
| 29. C4×#92418 | D4 | semidirect |
| 47. C42×C61 | M16 | semidirect |
| 73. #92418 | #127 | semidirect |
| 82. C4×C61 | #436 | semidirect |
| 89. #1842 | D61 | semidirect |
| 106. C61 | #21681 | semidirect |
| 143. C42 | #11758189 | semidirect |
| 172. C4 | #16839839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839839 | 2 |
| C4×#14519774 | 2 |
| #21446612 | 2 |
| C42×#92418 | 2 |
| C61×#1842 | 2 |
| #21681 | 61 |