Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
894 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 210 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 | #120 |
| commutator | C23 | C22×C8×C137 |
| Frattini, cosocle | C22×C8 | C23×C137 |
| socle | C2×C137 | #1779 |
| prime radical | #585×C137 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C137 ◁ C22×C8×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2115×C137 | C2 | semidirect |
| 3. #2113×C137 | C2 | semidirect |
| 9. C2×M32×C137 | C22 | semidirect |
| 10. C22×C16×C137 | C22 | semidirect |
| 86. #12684 | C137 | direct (N × H) |
| 87. C137 | #12684 | direct (N × H) |
| 89. #2115 | C2×C137 | semidirect |
| 90. #2113 | C2×C137 | semidirect |
| 96. C2×M32 | C22×C137 | semidirect |
| 97. C22×C16 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3573×C137 | 2 |
| #2115×C137 | 2 |
| #2113×C137 | 2 |
| #12684 | 137 |