Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
808 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 808 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×C137 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| prime radical | C23×C137 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1636×C137 | C2 | semidirect |
| 133. #18732 | C137 | direct (N × H) |
| 134. C137 | #18732 | direct (N × H) |
| 138. #1636 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3556×C137 | 2 |
| #3230×C137 | 2 |
| #3139×C137 | 2 |
| #1636×C137 | 2 |
| #1544×C137 | 2 |
| #1485×C137 | 2 |
| #18732 | 137 |