Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
256 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C139 |
| prime radical | #2206×C139 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C42×C139 ◁ C82×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2224×C139 | C2 | semidirect |
| 3. #1706×C139 | C2 | semidirect |
| 4. C8×D8×C139 | C2 | semidirect |
| 5. #1367×C139 | C2 | semidirect |
| 6. #1364×C139 | C2 | semidirect |
| 7. #1361×C139 | C2 | semidirect |
| 57. D8×C139 | SD16 | semidirect |
| 94. C8×C139 | D16 | semidirect |
| 116. #12416 | C139 | direct (N × H) |
| 117. C139 | #12416 | direct (N × H) |
| 118. #2224 | C2×C139 | semidirect |
| 120. #1706 | C2×C139 | semidirect |
| 121. C8×D8 | C2×C139 | semidirect |
| 122. #1367 | C2×C139 | semidirect |
| 123. #1364 | C2×C139 | semidirect |
| 124. #1361 | C2×C139 | semidirect |
| 174. D8 | SD16×C139 | semidirect |
| 211. C8 | D16×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2224×C139 | 2 |
| #2206×C139 | 2 |
| #1706×C139 | 2 |
| C8×D8×C139 | 2 |
| #1367×C139 | 2 |
| #1364×C139 | 2 |
| #1361×C139 | 2 |
| #12416 | 139 |