Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
610 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C139 |
| prime radical | #3192×C139 | C2 |
| LCS | G ▷ C23×C4 ▷ 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 |
|---|---|---|
| 2. #3094×C139 | C2 | semidirect |
| 3. #2624×C139 | C2 | semidirect |
| 4. #1964×C139 | C2 | semidirect |
| 5. #1826×C139 | C2 | semidirect |
| 6. #1507×C139 | C2 | semidirect |
| 7. #1305×C139 | C2 | semidirect |
| 235. #9932 | C139 | direct (N × H) |
| 236. C139 | #9932 | direct (N × H) |
| 238. #3094 | C2×C139 | semidirect |
| 239. #2624 | C2×C139 | semidirect |
| 240. #1964 | C2×C139 | semidirect |
| 241. #1826 | C2×C139 | semidirect |
| 242. #1507 | C2×C139 | semidirect |
| 243. #1305 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3192×C139 | 2 |
| #3094×C139 | 2 |
| #2624×C139 | 2 |
| #1964×C139 | 2 |
| #1826×C139 | 2 |
| #1507×C139 | 2 |
| #1305×C139 | 2 |
| #9932 | 139 |