Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
406 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C139 | #124 |
| commutator | C22×C4 | C22×C4×C139 |
| Frattini, cosocle | C22×C8 | C23×C139 |
| socle | C2×C139 | #1955 |
| prime radical | #575×C139 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C139 ◁ C22×C8×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2151×C139 | C2 | semidirect |
| 3. C2×#350×C139 | C2 | semidirect |
| 4. #2115×C139 | C2 | semidirect |
| 5. #2110×C139 | C2 | semidirect |
| 111. #13199 | C139 | direct (N × H) |
| 112. C139 | #13199 | direct (N × H) |
| 114. #2151 | C2×C139 | semidirect |
| 115. C2×#350 | C2×C139 | semidirect |
| 116. #2115 | C2×C139 | semidirect |
| 117. #2110 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2955×C139 | 2 |
| #2151×C139 | 2 |
| C2×#350×C139 | 2 |
| #2115×C139 | 2 |
| #2110×C139 | 2 |
| #13199 | 139 |