Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
542 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C139 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C139 |
| prime radical | C22×D4×C139 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#501×C139 | C2 | semidirect |
| 4. #1960×C139 | C2 | semidirect |
| 5. C2×#330×C139 | C2 | semidirect |
| 7. #1295×C139 | C2 | semidirect |
| 191. #10086 | C139 | direct (N × H) |
| 192. C139 | #10086 | direct (N × H) |
| 193. C2×#501 | C2×C139 | semidirect |
| 196. #1960 | C2×C139 | semidirect |
| 197. C2×#330 | C2×C139 | semidirect |
| 199. #1295 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#501×C139 | 2 |
| C2×#489×C139 | 2 |
| #2820×C139 | 2 |
| #1960×C139 | 2 |
| C2×#330×C139 | 2 |
| C2×#329×C139 | 2 |
| #1295×C139 | 2 |
| #10086 | 139 |