Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
298 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C139 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C22×C4×C139 ◁ C22×C8×C139 ◁ C22×C16×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#508×C139 | C2 | semidirect |
| 2. C2×SD64×C139 | C2 | semidirect |
| 3. C2×D32×C139 | C2 | semidirect |
| 4. #2215×C139 | C2 | semidirect |
| 5. #1416×C139 | C2 | semidirect |
| 6. #1415×C139 | C2 | semidirect |
| 7. C22⋊C32×C139 | C2 | semidirect |
| 33. Q32×C139 | D4 | semidirect |
| 38. D16×C139 | D4 | semidirect |
| 114. #13663 | C139 | direct (N × H) |
| 115. C139 | #13663 | direct (N × H) |
| 116. C2×#508 | C2×C139 | semidirect |
| 117. C2×SD64 | C2×C139 | semidirect |
| 118. C2×D32 | C2×C139 | semidirect |
| 119. #2215 | C2×C139 | semidirect |
| 120. #1416 | C2×C139 | semidirect |
| 121. #1415 | C2×C139 | semidirect |
| 122. C22⋊C32 | C2×C139 | semidirect |
| 148. Q32 | D4×C139 | semidirect |
| 153. D16 | D4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508×C139 | 2 |
| C2×SD64×C139 | 2 |
| C2×D32×C139 | 2 |
| #2215×C139 | 2 |
| #1416×C139 | 2 |
| #1415×C139 | 2 |
| C22⋊C32×C139 | 2 |
| #13663 | 139 |