Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
1278 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C139 |
| prime radical | #585×C139 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C22×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3059×C139 | C2 | semidirect |
| 4. #1909×C139 | C2 | semidirect |
| 5. #1812×C139 | C2 | semidirect |
| 7. C22×Q16×C139 | C22 | semidirect |
| 16. #427×C139 | C22 | semidirect |
| 17. #419×C139 | C22 | semidirect |
| 19. H(3,ℤ/4)×C139 | C22 | semidirect |
| 116. #32949 | C139 | direct (N × H) |
| 117. C139 | #32949 | direct (N × H) |
| 119. #3059 | C2×C139 | semidirect |
| 121. #1909 | C2×C139 | semidirect |
| 122. #1812 | C2×C139 | semidirect |
| 124. C22×Q16 | C22×C139 | semidirect |
| 133. #427 | C22×C139 | semidirect |
| 134. #419 | C22×C139 | semidirect |
| 136. H(3,ℤ/4) | C22×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3573×C139 | 2 |
| #3059×C139 | 2 |
| #3028×C139 | 2 |
| #1909×C139 | 2 |
| #1812×C139 | 2 |
| #32949 | 139 |