Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
370 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 370 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 | #481 |
| commutator | C2×C8 | C22×C4×C139 |
| Frattini, cosocle | C22×C8 | C23×C139 |
| socle | C2×C139 | #1824 |
| prime radical | C24×C139 | Q16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C139 ◁ C22×C4×C139 ◁ C22×M16×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1388×C139 | C2 | semidirect |
| 5. #1385×C139 | C2 | semidirect |
| 113. #12876 | C139 | direct (N × H) |
| 114. C139 | #12876 | direct (N × H) |
| 118. #1388 | C2×C139 | semidirect |
| 119. #1385 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#430×C139 | 2 |
| C2×#349×C139 | 2 |
| #1811×C139 | 2 |
| #1388×C139 | 2 |
| #1385×C139 | 2 |
| #12876 | 139 |