Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
336 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #120 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| socle | C22×C61 | #385 |
| prime radical | C23×C61 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. C61×#330 | C4 | semidirect |
| 18. C61×#330 | C4 | semidirect |
| 19. C61×#330 | C4 | semidirect |
| 84. #8919 | C61 | direct (N × H) |
| 115. #330 | C4×C61 | semidirect |
| 116. #330 | C4×C61 | semidirect |
| 117. #330 | C4×C61 | semidirect |
| 118. C61 | #8919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2987 | 2 |
| C61×#1995 | 2 |
| C61×#1569 | 2 |
| C61×#1526 | 2 |
| C61×#1300 | 2 |
| #8919 | 61 |