Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #102 |
| commutator | C2×C8 | C42×C61 |
| Frattini, cosocle | C23×C8 | C22×C61 |
| socle | C22×C61 | #340 |
| prime radical | C24×C61 | SD16 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C23×C4×C61 ◁ C23×C8×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×#108×C61 | C4 | semidirect |
| 10. C61×C22⋊C16 | C4 | semidirect |
| 88. #7260 | C61 | direct (N × H) |
| 118. C2×#108 | C4×C61 | semidirect |
| 121. C22⋊C16 | C4×C61 | semidirect |
| 125. C61 | #7260 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C61×C22⋊C16 | 2 |
| C61×#1810 | 2 |
| C61×#1735 | 2 |
| #7260 | 61 |