Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
520 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 520 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 | C4×C139 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C139 |
| socle | C2×C139 | #1999 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C139 ◁ C22×C4×C139 ◁ C2×#131×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3414×C139 | C2 | semidirect |
| 2. #3067×C139 | C2 | semidirect |
| 3. C2×#359×C139 | C2 | semidirect |
| 4. #2113×C139 | C2 | semidirect |
| 5. #1385×C139 | C2 | semidirect |
| 136. #13312 | C139 | direct (N × H) |
| 137. C139 | #13312 | direct (N × H) |
| 138. #3414 | C2×C139 | semidirect |
| 139. #3067 | C2×C139 | semidirect |
| 140. C2×#359 | C2×C139 | semidirect |
| 141. #2113 | C2×C139 | semidirect |
| 142. #1385 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3414×C139 | 2 |
| #3067×C139 | 2 |
| C2×#359×C139 | 2 |
| #2113×C139 | 2 |
| #1385×C139 | 2 |
| #13312 | 139 |