Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
596 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 206 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C139 |
| prime radical | C22×D4×C139 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ #376×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2645×C139 | C2 | semidirect |
| 3. #2088×C139 | C2 | semidirect |
| 4. #2066×C139 | C2 | semidirect |
| 7. #1843×C139 | C2 | semidirect |
| 116. #32868 | C139 | direct (N × H) |
| 117. C139 | #32868 | direct (N × H) |
| 118. #2645 | C2×C139 | semidirect |
| 120. #2088 | C2×C139 | semidirect |
| 121. #2066 | C2×C139 | semidirect |
| 124. #1843 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2645×C139 | 2 |
| #2644×C139 | 2 |
| #2088×C139 | 2 |
| #2066×C139 | 2 |
| #2065×C139 | 2 |
| #2055×C139 | 2 |
| #1843×C139 | 2 |
| #32868 | 139 |