Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
502 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #120 |
| commutator | C42 | C22×C4×C139 |
| Frattini, cosocle | C2×C42 | C23×C139 |
| socle | C22×C139 | #386 |
| prime radical | #3150×C139 | C2 |
| LCS | G ▷ 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. #2980×C139 | C2 | semidirect |
| 3. #1543×C139 | C2 | semidirect |
| 4. #1496×C139 | C2 | semidirect |
| 5. #1302×C139 | C2 | semidirect |
| 129. #9007 | C139 | direct (N × H) |
| 130. C139 | #9007 | direct (N × H) |
| 132. #2980 | C2×C139 | semidirect |
| 133. #1543 | C2×C139 | semidirect |
| 134. #1496 | C2×C139 | semidirect |
| 135. #1302 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3150×C139 | 2 |
| #2980×C139 | 2 |
| #1543×C139 | 2 |
| #1496×C139 | 2 |
| #1302×C139 | 2 |
| #9007 | 139 |