Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
290 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C139 |
| prime radical | #466×C139 | C22 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C22×C4×C139 ◁ #424×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2236×C139 | C2 | semidirect |
| 4. #2089×C139 | C2 | semidirect |
| 5. #1350×C139 | C2 | semidirect |
| 7. #1323×C139 | C2 | semidirect |
| 142. #12297 | C139 | direct (N × H) |
| 143. C139 | #12297 | direct (N × H) |
| 145. #2236 | C2×C139 | semidirect |
| 147. #2089 | C2×C139 | semidirect |
| 148. #1350 | C2×C139 | semidirect |
| 150. #1323 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3262×C139 | 2 |
| #2236×C139 | 2 |
| #2232×C139 | 2 |
| #2089×C139 | 2 |
| #1350×C139 | 2 |
| #1349×C139 | 2 |
| #1323×C139 | 2 |
| #12297 | 139 |