Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
780 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C2×#121×C139 | C22 |
| 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 |
|---|---|---|
| 3. #2434×C139 | C2 | semidirect |
| 4. #1784×C139 | C2 | semidirect |
| 5. #1508×C139 | C2 | semidirect |
| 7. #1297×C139 | C2 | semidirect |
| 223. #10330 | C139 | direct (N × H) |
| 224. C139 | #10330 | direct (N × H) |
| 227. #2434 | C2×C139 | semidirect |
| 228. #1784 | C2×C139 | semidirect |
| 229. #1508 | C2×C139 | semidirect |
| 231. #1297 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3193×C139 | 2 |
| #2436×C139 | 2 |
| #2434×C139 | 2 |
| #1784×C139 | 2 |
| #1508×C139 | 2 |
| #1507×C139 | 2 |
| #1297×C139 | 2 |
| #10330 | 139 |