Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
884 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 230 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| prime radical | C2×#127×C137 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3556×C137 | C2 | semidirect |
| 4. #1626×C137 | C2 | semidirect |
| 5. #1544×C137 | C2 | semidirect |
| 6. #1485×C137 | C2 | semidirect |
| 10. #557×C137 | C22 | semidirect |
| 25. #332×C137 | C22 | semidirect |
| 26. Q8⋊C8×C137 | C22 | semidirect |
| 141. #18731 | C137 | direct (N × H) |
| 142. C137 | #18731 | direct (N × H) |
| 143. #3556 | C2×C137 | semidirect |
| 146. #1626 | C2×C137 | semidirect |
| 147. #1544 | C2×C137 | semidirect |
| 148. #1485 | C2×C137 | semidirect |
| 152. #557 | C22×C137 | semidirect |
| 167. #332 | C22×C137 | semidirect |
| 168. Q8⋊C8 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3556×C137 | 2 |
| #3208×C137 | 2 |
| #3138×C137 | 2 |
| #1626×C137 | 2 |
| #1544×C137 | 2 |
| #1485×C137 | 2 |
| #18731 | 137 |