Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C139 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C139 |
| prime radical | #3213×C139 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3216×C139 | C2 | semidirect |
| 3. #3140×C139 | C2 | semidirect |
| 4. #1497×C139 | C2 | semidirect |
| 5. #1484×C139 | C2 | semidirect |
| 6. #1469×C139 | C2 | semidirect |
| 7. #1291×C139 | C2 | semidirect |
| 195. #10124 | C139 | direct (N × H) |
| 196. C139 | #10124 | direct (N × H) |
| 197. #3216 | C2×C139 | semidirect |
| 199. #3140 | C2×C139 | semidirect |
| 200. #1497 | C2×C139 | semidirect |
| 201. #1484 | C2×C139 | semidirect |
| 202. #1469 | C2×C139 | semidirect |
| 203. #1291 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3216×C139 | 2 |
| #3213×C139 | 2 |
| #3140×C139 | 2 |
| #1497×C139 | 2 |
| #1484×C139 | 2 |
| #1469×C139 | 2 |
| #1291×C139 | 2 |
| #10124 | 139 |