Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1154 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 150 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×#99 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C22×Q8 | C23×C61 |
| prime radical | C2×C61×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C22×#41×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C61×#355 | C2 | semidirect |
| 3. C61×#1785 | C2 | semidirect |
| 12. C2×#101×C61 | C22 | semidirect |
| 129. #12703 | C61 | direct (N × H) |
| 152. C2×#355 | C2×C61 | semidirect |
| 153. #1785 | C2×C61 | semidirect |
| 169. C2×#101 | C22×C61 | semidirect |
| 173. C61 | #12703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C61×#535 | 2 |
| C2×C61×#355 | 2 |
| C61×#1785 | 2 |
| #12703 | 61 |