Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C61 |
| prime radical | C61×#2017 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×M16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3202 | C2 | semidirect |
| 2. C61×#2191 | C2 | semidirect |
| 4. C61×#1342 | C2 | semidirect |
| 5. C61×#1321 | C2 | semidirect |
| 126. #12118 | C61 | direct (N × H) |
| 141. #3202 | C2×C61 | semidirect |
| 142. #2191 | C2×C61 | semidirect |
| 144. #1342 | C2×C61 | semidirect |
| 145. #1321 | C2×C61 | semidirect |
| 164. C61 | #12118 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3202 | 2 |
| C61×#2191 | 2 |
| C61×#2017 | 2 |
| C61×#1342 | 2 |
| C61×#1321 | 2 |
| #12118 | 61 |