Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
770 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 770 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 | C2×C42 | C23×C139 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3213×C139 | C2 | semidirect |
| 2. #3151×C139 | C2 | semidirect |
| 3. #2657×C139 | C2 | semidirect |
| 4. #1555×C139 | C2 | semidirect |
| 5. #1527×C139 | C2 | semidirect |
| 6. #1505×C139 | C2 | semidirect |
| 7. #1300×C139 | C2 | semidirect |
| 44. C4⋊Q8×C139 | D4 | semidirect |
| 50. #127×C139 | D4 | semidirect |
| 67. C4⋊C8×C139 | D4 | semidirect |
| 74. #97×C139 | D4 | semidirect |
| 211. #10088 | C139 | direct (N × H) |
| 212. C139 | #10088 | direct (N × H) |
| 213. #3213 | C2×C139 | semidirect |
| 214. #3151 | C2×C139 | semidirect |
| 215. #2657 | C2×C139 | semidirect |
| 216. #1555 | C2×C139 | semidirect |
| 217. #1527 | C2×C139 | semidirect |
| 218. #1505 | C2×C139 | semidirect |
| 219. #1300 | C2×C139 | semidirect |
| 256. C4⋊Q8 | D4×C139 | semidirect |
| 262. #127 | D4×C139 | semidirect |
| 279. C4⋊C8 | D4×C139 | semidirect |
| 286. #97 | D4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3213×C139 | 2 |
| #3151×C139 | 2 |
| #2657×C139 | 2 |
| #1555×C139 | 2 |
| #1527×C139 | 2 |
| #1505×C139 | 2 |
| #1300×C139 | 2 |
| #10088 | 139 |