Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
878 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 878 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×C139 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C139 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3192×C139 | C2 | semidirect |
| 2. C2×#447×C139 | C2 | semidirect |
| 3. #1783×C139 | C2 | semidirect |
| 4. #1471×C139 | C2 | semidirect |
| 5. #1298×C139 | C2 | semidirect |
| 150. #9986 | C139 | direct (N × H) |
| 151. C139 | #9986 | direct (N × H) |
| 152. #3192 | C2×C139 | semidirect |
| 153. C2×#447 | C2×C139 | semidirect |
| 154. #1783 | C2×C139 | semidirect |
| 155. #1471 | C2×C139 | semidirect |
| 156. #1298 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3192×C139 | 2 |
| C2×#447×C139 | 2 |
| #1783×C139 | 2 |
| #1471×C139 | 2 |
| #1298×C139 | 2 |
| #9986 | 139 |