Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
724 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 106 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 | 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. C2×#451×C137 | C2 | semidirect |
| 4. #1784×C137 | C2 | semidirect |
| 5. #1472×C137 | C2 | semidirect |
| 7. #1298×C137 | C2 | semidirect |
| 215. #9989 | C137 | direct (N × H) |
| 216. C137 | #9989 | direct (N × H) |
| 218. C2×#451 | C2×C137 | semidirect |
| 220. #1784 | C2×C137 | semidirect |
| 221. #1472 | C2×C137 | semidirect |
| 223. #1298 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3193×C137 | 2 |
| C2×#451×C137 | 2 |
| C2×#448×C137 | 2 |
| #1784×C137 | 2 |
| #1472×C137 | 2 |
| #1471×C137 | 2 |
| #1298×C137 | 2 |
| #9989 | 137 |