Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
504 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C2×#99 |
| commutator | C2×C4 | C22×C8×C61 |
| Frattini, cosocle | C2×M16 | C23×C61 |
| socle | C2×C61 | C2×#323 |
| prime radical | C22×#41×C61 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ C22×M16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C61×#349 | C2 | semidirect |
| 3. C61×#1321 | C2 | semidirect |
| 13. C61×#349 | C22 | semidirect |
| 116. #11438 | C61 | direct (N × H) |
| 135. C2×#349 | C2×C61 | semidirect |
| 136. #1321 | C2×C61 | semidirect |
| 152. #349 | C22×C61 | semidirect |
| 153. C61 | #11438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2879 | 2 |
| C2×C61×#349 | 2 |
| C61×#1321 | 2 |
| #11438 | 61 |