Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
366 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C139 | #418 |
| commutator | C2×C8 | C22×C4×C139 |
| Frattini, cosocle | C22×C8 | C23×C139 |
| socle | C2×C139 | #1824 |
| prime radical | C2×#41×C139 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C139 ◁ C22×C4×C139 ◁ C2×#131×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1389×C139 | C2 | semidirect |
| 5. #1382×C139 | C2 | semidirect |
| 11. #430×C139 | C4 | semidirect |
| 97. #12877 | C139 | direct (N × H) |
| 98. C139 | #12877 | direct (N × H) |
| 102. #1389 | C2×C139 | semidirect |
| 103. #1382 | C2×C139 | semidirect |
| 109. #430 | C4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2916×C139 | 2 |
| #2113×C139 | 2 |
| #1812×C139 | 2 |
| #1389×C139 | 2 |
| #1382×C139 | 2 |
| #12877 | 139 |