Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
474 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #394 |
| commutator, Frattini, cosocle | C23×C4 | C23×C137 |
| prime radical | C2×#121×C137 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1901×C137 | C2 | semidirect |
| 4. #1851×C137 | C2 | semidirect |
| 5. #1508×C137 | C2 | semidirect |
| 7. #1293×C137 | C2 | semidirect |
| 221. #10558 | C137 | direct (N × H) |
| 222. C137 | #10558 | direct (N × H) |
| 224. #1901 | C2×C137 | semidirect |
| 226. #1851 | C2×C137 | semidirect |
| 227. #1508 | C2×C137 | semidirect |
| 229. #1293 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3187×C137 | 2 |
| #1901×C137 | 2 |
| #1900×C137 | 2 |
| #1851×C137 | 2 |
| #1508×C137 | 2 |
| #1507×C137 | 2 |
| #1293×C137 | 2 |
| #10558 | 137 |