Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 534 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, socle | C22×C31 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C31 |
| prime radical | C2×C31×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#3255 | C2 | semidirect |
| 5. C31×#1526 | C2 | semidirect |
| 6. C31×#1485 | C2 | semidirect |
| 7. C31×#1299 | C2 | semidirect |
| 124. #10113 | C31 | direct (N × H) |
| 161. #3255 | C2×C31 | semidirect |
| 165. #1526 | C2×C31 | semidirect |
| 166. #1485 | C2×C31 | semidirect |
| 167. #1299 | C2×C31 | semidirect |
| 260. C31 | #10113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3255 | 2 |
| C31×#3208 | 2 |
| C31×#3138 | 2 |
| C31×#1965 | 2 |
| C31×#1526 | 2 |
| C31×#1485 | 2 |
| C31×#1299 | 2 |
| #10113 | 31 |