Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
736 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C139 |
| prime radical | C2×#127×C139 | C22 |
| LCS | G ▷ 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. #3185×C139 | C2 | semidirect |
| 3. #1720×C139 | C2 | semidirect |
| 4. #1711×C139 | C2 | semidirect |
| 5. #1455×C139 | C2 | semidirect |
| 8. #498×C139 | C22 | semidirect |
| 9. #494×C139 | C22 | semidirect |
| 11. #487×C139 | C22 | semidirect |
| 18. #322×C139 | C22 | semidirect |
| 19. C82×C139 | C22 | semidirect |
| 77. #19753 | C139 | direct (N × H) |
| 78. C139 | #19753 | direct (N × H) |
| 79. #3185 | C2×C139 | semidirect |
| 81. #1720 | C2×C139 | semidirect |
| 82. #1711 | C2×C139 | semidirect |
| 83. #1455 | C2×C139 | semidirect |
| 86. #498 | C22×C139 | semidirect |
| 87. #494 | C22×C139 | semidirect |
| 89. #487 | C22×C139 | semidirect |
| 96. #322 | C22×C139 | semidirect |
| 97. C82 | C22×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3185×C139 | 2 |
| #3138×C139 | 2 |
| #1720×C139 | 2 |
| #1711×C139 | 2 |
| #1455×C139 | 2 |
| #19753 | 139 |