Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
742 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C23×C4 | C23×C139 |
| prime radical | #3006×C139 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3187×C139 | C2 | semidirect |
| 2. #3007×C139 | C2 | semidirect |
| 4. #1780×C139 | C2 | semidirect |
| 5. #1472×C139 | C2 | semidirect |
| 6. #1471×C139 | C2 | semidirect |
| 7. #1293×C139 | C2 | semidirect |
| 246. #9975 | C139 | direct (N × H) |
| 247. C139 | #9975 | direct (N × H) |
| 248. #3187 | C2×C139 | semidirect |
| 249. #3007 | C2×C139 | semidirect |
| 251. #1780 | C2×C139 | semidirect |
| 252. #1472 | C2×C139 | semidirect |
| 253. #1471 | C2×C139 | semidirect |
| 254. #1293 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3187×C139 | 2 |
| #3007×C139 | 2 |
| #3006×C139 | 2 |
| #1780×C139 | 2 |
| #1472×C139 | 2 |
| #1471×C139 | 2 |
| #1293×C139 | 2 |
| #9975 | 139 |