Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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 | #99 |
| commutator | C23 | C2×C16×C137 |
| Frattini, cosocle | C2×M32 | C22×C137 |
| socle | C2×C137 | #1322 |
| prime radical | C23×C137 | C2×C16 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C137 ◁ C2×C8×C137 ◁ C2×M32×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. #7365 | C137 | direct (N × H) |
| 51. C137 | #7365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2151×C137 | 2 |
| #1400×C137 | 2 |
| #7365 | 137 |