Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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 | 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 |
|---|---|---|
| 2. #1997×C137 | C2 | semidirect |
| 3. #1574×C137 | C2 | semidirect |
| 5. #1549×C137 | C2 | semidirect |
| 7. #1299×C137 | C2 | semidirect |
| 153. #10490 | C137 | direct (N × H) |
| 154. C137 | #10490 | direct (N × H) |
| 156. #1997 | C2×C137 | semidirect |
| 157. #1574 | C2×C137 | semidirect |
| 159. #1549 | C2×C137 | semidirect |
| 161. #1299 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3226×C137 | 2 |
| #1997×C137 | 2 |
| #1574×C137 | 2 |
| #1560×C137 | 2 |
| #1549×C137 | 2 |
| #1484×C137 | 2 |
| #1299×C137 | 2 |
| #10490 | 137 |