Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
186 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | #1677 |
| commutator, Frattini, cosocle | C4×C8 | C23×C137 |
| prime radical | #135×C137 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C2×C4×C137 ◁ C4×C8×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2245×C137 | C2 | semidirect |
| 5. #1369×C137 | C2 | semidirect |
| 6. #1366×C137 | C2 | semidirect |
| 7. #1358×C137 | C2 | semidirect |
| 92. #12466 | C137 | direct (N × H) |
| 93. C137 | #12466 | direct (N × H) |
| 94. #2245 | C2×C137 | semidirect |
| 98. #1369 | C2×C137 | semidirect |
| 99. #1366 | C2×C137 | semidirect |
| 100. #1358 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2245×C137 | 2 |
| #2231×C137 | 2 |
| #2214×C137 | 2 |
| #2171×C137 | 2 |
| #1369×C137 | 2 |
| #1366×C137 | 2 |
| #1358×C137 | 2 |
| #12466 | 137 |