Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
472 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C137 |
| prime radical | C22×D4×C137 | D4 |
| LCS | G ▷ C2×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. #3229×C137 | C2 | semidirect |
| 4. #1558×C137 | C2 | semidirect |
| 5. #1531×C137 | C2 | semidirect |
| 7. #1302×C137 | C2 | semidirect |
| 174. #10141 | C137 | direct (N × H) |
| 175. C137 | #10141 | direct (N × H) |
| 176. #3229 | C2×C137 | semidirect |
| 179. #1558 | C2×C137 | semidirect |
| 180. #1531 | C2×C137 | semidirect |
| 182. #1302 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3229×C137 | 2 |
| #3215×C137 | 2 |
| C2×#489×C137 | 2 |
| #1558×C137 | 2 |
| #1531×C137 | 2 |
| #1469×C137 | 2 |
| #1302×C137 | 2 |
| #10141 | 137 |