Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
1182 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C137 | C2×D4 |
| commutator | C2×C4 | C23×C4×C137 |
| Frattini, cosocle | C22×C4 | C24×C137 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C137 ◁ C22×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #1942×C137 | C2 | direct (N × H) |
| 14. C2×#107×C137 | C4 | semidirect |
| 51. #107×C137 | C2×C4 | semidirect |
| 82. C2×C8×C137 | C4⋊C4 | semidirect |
| 135. C8×C137 | C2×C4⋊C4 | semidirect |
| 159. C2×C137 | #1942 | direct (N × H) |
| 167. C2×#1942 | C137 | direct (N × H) |
| 168. C137 | C2×#1942 | direct (N × H) |
| 173. #1942 | C2×C137 | direct (N × H) |
| 182. C2×#107 | C4×C137 | semidirect |
| 219. #107 | C2×C4×C137 | semidirect |
| 250. C2×C8 | C4⋊C4×C137 | semidirect |
| 303. C8 | C2×C4⋊C4×C137 | semidirect |
| 327. C2 | #1942×C137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#107×C137 | 2 |
| C22×C4×C8×C137 | 2 |
| C2×#389×C137 | 2 |
| #1942×C137 | 2 |
| C2×#340×C137 | 2 |
| C2×#1942 | 137 |