Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
170 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C137 | #117 |
| commutator | C2×C4 | C22×C8×C137 |
| Frattini, cosocle | C2×C16 | C23×C137 |
| socle | C2×C137 | #2163 |
| prime radical | C23×C137 | M32 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C137 ◁ #346×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1422×C137 | C2 | semidirect |
| 4. #1398×C137 | C2 | semidirect |
| 67. #13642 | C137 | direct (N × H) |
| 68. C137 | #13642 | direct (N × H) |
| 70. #1422 | C2×C137 | semidirect |
| 72. #1398 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×M32×C137 | 2 |
| #1422×C137 | 2 |
| #1400×C137 | 2 |
| #1398×C137 | 2 |
| #13642 | 137 |