Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
226 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 226 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 | C2×C4×C137 | C2×D8 |
| commutator | C2×C8 | C22×C4×C137 |
| Frattini, cosocle | C4×C8 | C23×C137 |
| socle | C22×C137 | C4×D8 |
| prime radical | C2×D8×C137 | C2×C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C137 ◁ C4×C8×C137 ◁ C82×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1591×C137 | C2 | semidirect |
| 4. #1372×C137 | C2 | semidirect |
| 5. #1332×C137 | C2 | semidirect |
| 7. #1312×C137 | C2 | semidirect |
| 86. C8×C137 | SD32 | semidirect |
| 105. #12070 | C137 | direct (N × H) |
| 106. C137 | #12070 | direct (N × H) |
| 108. #1591 | C2×C137 | semidirect |
| 110. #1372 | C2×C137 | semidirect |
| 111. #1332 | C2×C137 | semidirect |
| 113. #1312 | C2×C137 | semidirect |
| 192. C8 | SD32×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×SD32×C137 | 2 |
| #1591×C137 | 2 |
| C8×D8×C137 | 2 |
| #1372×C137 | 2 |
| #1332×C137 | 2 |
| #1331×C137 | 2 |
| #1312×C137 | 2 |
| #12070 | 137 |