Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
344 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #1598 |
| commutator, Frattini, cosocle | C2×M16 | C23×C61 |
| prime radical | C61×#2190 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×M16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3263 | C2 | semidirect |
| 2. C61×#2191 | C2 | semidirect |
| 4. C61×#2053 | C2 | semidirect |
| 5. C61×#1340 | C2 | semidirect |
| 6. C61×#1339 | C2 | semidirect |
| 7. C61×#1328 | C2 | semidirect |
| 148. #12172 | C61 | direct (N × H) |
| 167. #3263 | C2×C61 | semidirect |
| 168. #2191 | C2×C61 | semidirect |
| 170. #2053 | C2×C61 | semidirect |
| 171. #1340 | C2×C61 | semidirect |
| 172. #1339 | C2×C61 | semidirect |
| 173. #1328 | C2×C61 | semidirect |
| 198. C61 | #12172 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3263 | 2 |
| C61×#2191 | 2 |
| C61×#2190 | 2 |
| C61×#2053 | 2 |
| C61×#1340 | 2 |
| C61×#1339 | 2 |
| C61×#1328 | 2 |
| #12172 | 61 |