Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
588 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 154 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 | C2×#127×C139 | C22 |
| 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. #2551×C139 | C2 | semidirect |
| 4. #1296×C139 | C2 | semidirect |
| 5. #1279×C139 | C2 | semidirect |
| 26. #127×C139 | Q8 | semidirect |
| 137. #10348 | C139 | direct (N × H) |
| 138. C139 | #10348 | direct (N × H) |
| 139. #2551 | C2×C139 | semidirect |
| 142. #1296 | C2×C139 | semidirect |
| 143. #1279 | C2×C139 | semidirect |
| 164. #127 | Q8×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2551×C139 | 2 |
| #1982×C139 | 2 |
| #1957×C139 | 2 |
| #1296×C139 | 2 |
| #1279×C139 | 2 |
| #10348 | 139 |