Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
682 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #386 |
| commutator | C24 | C22×C4×C139 |
| Frattini, cosocle | C23×C4 | C23×C139 |
| prime radical | C22×D4×C139 | C2×C4 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1784×C139 | C2 | semidirect |
| 5. #1305×C139 | C2 | semidirect |
| 135. C2×C4×C139 | #101 | semidirect |
| 171. #9506 | C139 | direct (N × H) |
| 172. C139 | #9506 | direct (N × H) |
| 175. #1784 | C2×C139 | semidirect |
| 177. #1305 | C2×C139 | semidirect |
| 307. C2×C4 | #101×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2975×C139 | 2 |
| #2409×C139 | 2 |
| #1784×C139 | 2 |
| #1465×C139 | 2 |
| #1305×C139 | 2 |
| #9506 | 139 |