Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
306 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2163×C137 | C2 | semidirect |
| 3. #1323×C137 | C2 | semidirect |
| 102. #11463 | C137 | direct (N × H) |
| 103. C137 | #11463 | direct (N × H) |
| 105. #2163 | C2×C137 | semidirect |
| 106. #1323 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2922×C137 | 2 |
| #2163×C137 | 2 |
| #1323×C137 | 2 |
| #1315×C137 | 2 |
| #11463 | 137 |