Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
302 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 302 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.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×D16 |
| commutator | C16 | C22×C4×C137 |
| Frattini, cosocle | C2×C16 | C23×C137 |
| prime radical | C2×#508×C137 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C22×C4×C137 ◁ C22×C8×C137 ◁ C22×C16×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M64×C137 | C2 | semidirect |
| 3. C2×#366×C137 | C2 | semidirect |
| 4. #1416×C137 | C2 | semidirect |
| 5. #1415×C137 | C2 | semidirect |
| 8. #508×C137 | C4 | semidirect |
| 27. Q32×C137 | C2×C4 | semidirect |
| 30. D16×C137 | C2×C4 | semidirect |
| 95. #13616 | C137 | direct (N × H) |
| 96. C137 | #13616 | direct (N × H) |
| 98. C2×M64 | C2×C137 | semidirect |
| 99. C2×#366 | C2×C137 | semidirect |
| 100. #1416 | C2×C137 | semidirect |
| 101. #1415 | C2×C137 | semidirect |
| 104. #508 | C4×C137 | semidirect |
| 123. Q32 | C2×C4×C137 | semidirect |
| 126. D16 | C2×C4×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508×C137 | 2 |
| C2×M64×C137 | 2 |
| C2×#366×C137 | 2 |
| #1416×C137 | 2 |
| #1415×C137 | 2 |
| #13616 | 137 |