Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1176 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 242 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C61 |
| prime radical | C61×#3459 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C61×#2486 | C2 | semidirect |
| 3. C61×#2030 | C2 | semidirect |
| 4. C61×#2022 | C2 | semidirect |
| 5. C61×#1799 | C2 | semidirect |
| 136. #29685 | C61 | direct (N × H) |
| 157. #2486 | C2×C61 | semidirect |
| 158. #2030 | C2×C61 | semidirect |
| 159. #2022 | C2×C61 | semidirect |
| 160. #1799 | C2×C61 | semidirect |
| 184. C61 | #29685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3459 | 2 |
| C61×#2486 | 2 |
| C61×#2030 | 2 |
| C61×#2022 | 2 |
| C61×#1799 | 2 |
| #29685 | 61 |