Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 996 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 | #3151×C137 | C2 |
| 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. #3550×C137 | C2 | semidirect |
| 3. #3138×C137 | C2 | semidirect |
| 4. #1657×C137 | C2 | semidirect |
| 5. #1526×C137 | C2 | semidirect |
| 6. #1525×C137 | C2 | semidirect |
| 8. #563×C137 | C22 | semidirect |
| 27. #330×C137 | C22 | semidirect |
| 28. #329×C137 | C22 | semidirect |
| 165. #19077 | C137 | direct (N × H) |
| 166. C137 | #19077 | direct (N × H) |
| 167. #3550 | C2×C137 | semidirect |
| 169. #3138 | C2×C137 | semidirect |
| 170. #1657 | C2×C137 | semidirect |
| 171. #1526 | C2×C137 | semidirect |
| 172. #1525 | C2×C137 | semidirect |
| 174. #563 | C22×C137 | semidirect |
| 193. #330 | C22×C137 | semidirect |
| 194. #329 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3550×C137 | 2 |
| #3151×C137 | 2 |
| #3138×C137 | 2 |
| #1657×C137 | 2 |
| #1526×C137 | 2 |
| #1525×C137 | 2 |
| #19077 | 137 |