Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
460 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 460 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 | C2×C4×C139 | #120 |
| commutator | C22×C4 | C22×C4×C139 |
| Frattini, cosocle | C23×C4 | C23×C139 |
| socle | C22×C139 | #385 |
| prime radical | C22×D4×C139 | Q8 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C139 ◁ C23×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1855×C139 | C2 | semidirect |
| 5. #1298×C139 | C2 | semidirect |
| 98. C23×C139 | #108 | semidirect |
| 155. #8859 | C139 | direct (N × H) |
| 156. C139 | #8859 | direct (N × H) |
| 159. #1855 | C2×C139 | semidirect |
| 161. #1298 | C2×C139 | semidirect |
| 254. C23 | #108×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2973×C139 | 2 |
| #1870×C139 | 2 |
| #1855×C139 | 2 |
| #1459×C139 | 2 |
| #1298×C139 | 2 |
| #8859 | 139 |