Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
468 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 468 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 | #532×C137 | C22 |
| 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 |
|---|---|---|
| 3. C2×#501×C137 | C2 | semidirect |
| 4. #1556×C137 | C2 | semidirect |
| 6. #1470×C137 | C2 | semidirect |
| 7. #1302×C137 | C2 | semidirect |
| 169. #10138 | C137 | direct (N × H) |
| 170. C137 | #10138 | direct (N × H) |
| 173. C2×#501 | C2×C137 | semidirect |
| 174. #1556 | C2×C137 | semidirect |
| 176. #1470 | C2×C137 | semidirect |
| 177. #1302 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3234×C137 | 2 |
| #3206×C137 | 2 |
| C2×#501×C137 | 2 |
| #1556×C137 | 2 |
| #1530×C137 | 2 |
| #1470×C137 | 2 |
| #1302×C137 | 2 |
| #10138 | 137 |