Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
542 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 542 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 | C2×C42 | C23×C139 |
| prime radical | C2×#127×C139 | C22 |
| 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. #3236×C139 | C2 | semidirect |
| 5. #1528×C139 | C2 | semidirect |
| 6. #1506×C139 | C2 | semidirect |
| 7. #1300×C139 | C2 | semidirect |
| 178. #10097 | C139 | direct (N × H) |
| 179. C139 | #10097 | direct (N × H) |
| 180. #3236 | C2×C139 | semidirect |
| 184. #1528 | C2×C139 | semidirect |
| 185. #1506 | C2×C139 | semidirect |
| 186. #1300 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3236×C139 | 2 |
| #3138×C139 | 2 |
| #2641×C139 | 2 |
| #1555×C139 | 2 |
| #1528×C139 | 2 |
| #1506×C139 | 2 |
| #1300×C139 | 2 |
| #10097 | 139 |