Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
330 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 330 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 | C2×C4×C139 | #124 |
| commutator, Frattini, cosocle | C2×C42 | C23×C139 |
| socle | C22×C139 | #397 |
| prime radical | #532×C139 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1843×C139 | C2 | semidirect |
| 4. #1301×C139 | C2 | semidirect |
| 5. #1274×C139 | C2 | semidirect |
| 116. #10627 | C139 | direct (N × H) |
| 117. C139 | #10627 | direct (N × H) |
| 119. #1843 | C2×C139 | semidirect |
| 121. #1301 | C2×C139 | semidirect |
| 122. #1274 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1963×C139 | 2 |
| #1843×C139 | 2 |
| #1540×C139 | 2 |
| #1301×C139 | 2 |
| #1274×C139 | 2 |
| #10627 | 139 |