Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 414 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 | C22×C139 | #394 |
| 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 |
|---|---|---|
| 2. #1983×C139 | C2 | semidirect |
| 3. #1573×C139 | C2 | semidirect |
| 4. #1551×C139 | C2 | semidirect |
| 5. #1502×C139 | C2 | semidirect |
| 6. #1469×C139 | C2 | semidirect |
| 7. #1285×C139 | C2 | semidirect |
| 193. #10508 | C139 | direct (N × H) |
| 194. C139 | #10508 | direct (N × H) |
| 196. #1983 | C2×C139 | semidirect |
| 197. #1573 | C2×C139 | semidirect |
| 198. #1551 | C2×C139 | semidirect |
| 199. #1502 | C2×C139 | semidirect |
| 200. #1469 | C2×C139 | semidirect |
| 201. #1285 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3213×C139 | 2 |
| #1983×C139 | 2 |
| #1573×C139 | 2 |
| #1551×C139 | 2 |
| #1502×C139 | 2 |
| #1469×C139 | 2 |
| #1285×C139 | 2 |
| #10508 | 139 |