Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #2127 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C4⋊Q8 | C23×C61 |
| prime radical | C2×#41×C61 | D4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C61 ◁ C22×C4×C61 ◁ C61×#536 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C61×#1413 | C2 | semidirect |
| 5. C61×#1411 | C2 | semidirect |
| 123. #13612 | C61 | direct (N × H) |
| 141. #1413 | C2×C61 | semidirect |
| 142. #1411 | C2×C61 | semidirect |
| 164. C61 | #13612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3223 | 2 |
| C61×#2135 | 2 |
| C61×#2133 | 2 |
| C61×#1413 | 2 |
| C61×#1411 | 2 |
| #13612 | 61 |