Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
466 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 146 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 | #1893 |
| commutator | C2×C8 | C22×C4×C139 |
| Frattini, cosocle | C22×C8 | C23×C139 |
| prime radical | #3060×C139 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C22×C4×C139 ◁ C2×#131×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3407×C139 | C2 | semidirect |
| 3. #2143×C139 | C2 | semidirect |
| 4. #1813×C139 | C2 | semidirect |
| 5. #1383×C139 | C2 | semidirect |
| 45. C2×C16×C139 | D4 | semidirect |
| 138. #13076 | C139 | direct (N × H) |
| 139. C139 | #13076 | direct (N × H) |
| 140. #3407 | C2×C139 | semidirect |
| 142. #2143 | C2×C139 | semidirect |
| 143. #1813 | C2×C139 | semidirect |
| 144. #1383 | C2×C139 | semidirect |
| 184. C2×C16 | D4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3407×C139 | 2 |
| #3060×C139 | 2 |
| #2143×C139 | 2 |
| #1813×C139 | 2 |
| #1383×C139 | 2 |
| #13076 | 139 |