Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1206 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 158 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×D4 | C23×C61 |
| prime radical | C23×D4×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C24×C61 ◁ C23×D4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C61×#354 | C2 | semidirect |
| 4. C23×Q8×C61 | C4 | semidirect |
| 8. C2×#124×C61 | C4 | semidirect |
| 11. C22×C42×C61 | C4 | semidirect |
| 60. C2×Q8×C61 | C22⋊C4 | semidirect |
| 91. C42×C61 | C22⋊C4 | semidirect |
| 132. #12694 | C61 | direct (N × H) |
| 147. C22×C61 | #354 | semidirect |
| 157. C2×#354 | C2×C61 | semidirect |
| 166. C23×Q8 | C4×C61 | semidirect |
| 170. C2×#124 | C4×C61 | semidirect |
| 173. C22×C42 | C4×C61 | semidirect |
| 178. C61 | #12694 | direct (N × H) |
| 223. C2×Q8 | C22⋊C4×C61 | semidirect |
| 254. C42 | C22⋊C4×C61 | semidirect |
| 309. C22 | C61×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#124×C61 | 2 |
| C2×C61×#354 | 2 |
| C61×#1781 | 2 |
| #12694 | 61 |