Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3274 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 3274 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C61 | C24 |
| commutator | C23 | C23×C4×C61 |
| Frattini, cosocle | C24 | C24×C61 |
| prime radical | C22×#120×C61 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C61×#379 | C2 | semidirect |
| 3. C61×#1440 | C2 | semidirect |
| 4. C61×#1438 | C2 | semidirect |
| 8. C2×#120×C61 | C4 | semidirect |
| 11. C22×C22⋊C4×C61 | C22 | semidirect |
| 13. C2×#95×C61 | C22 | semidirect |
| 39. C24×C61 | C22⋊C4 | semidirect |
| 82. #14657 | C61 | direct (N × H) |
| 99. C2×#379 | C2×C61 | semidirect |
| 100. #1440 | C2×C61 | semidirect |
| 101. #1438 | C2×C61 | semidirect |
| 110. C2×#120 | C4×C61 | semidirect |
| 113. C22×C22⋊C4 | C22×C61 | semidirect |
| 115. C2×#95 | C22×C61 | semidirect |
| 116. C61 | #14657 | direct (N × H) |
| 142. C24 | C22⋊C4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#120×C61 | 2 |
| C2×C61×#379 | 2 |
| C61×#1440 | 2 |
| C61×#1438 | 2 |
| #14657 | 61 |