Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #1505 |
| commutator | C2×C8 | C22×C4×C139 |
| Frattini, cosocle | C2×M16 | C23×C139 |
| prime radical | C23×C139 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C2×C4×C139 ◁ #405×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #499×C139 | C4 | semidirect |
| 8. #494×C139 | C4 | semidirect |
| 12. #441×C139 | C4 | semidirect |
| 108. #11771 | C139 | direct (N × H) |
| 109. C139 | #11771 | direct (N × H) |
| 116. #499 | C4×C139 | semidirect |
| 117. #494 | C4×C139 | semidirect |
| 121. #441 | C4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3177×C139 | 2 |
| #2166×C139 | 2 |
| #1747×C139 | 2 |
| #1342×C139 | 2 |
| #1340×C139 | 2 |
| #11771 | 139 |