Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
402 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C137 |
| prime radical | #3203×C137 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C22×C4×C137 ◁ #408×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2188×C137 | C2 | semidirect |
| 3. #2185×C137 | C2 | semidirect |
| 4. #2020×C137 | C2 | semidirect |
| 5. #1350×C137 | C2 | semidirect |
| 6. #1349×C137 | C2 | semidirect |
| 7. #1315×C137 | C2 | semidirect |
| 177. #12113 | C137 | direct (N × H) |
| 178. C137 | #12113 | direct (N × H) |
| 180. #2188 | C2×C137 | semidirect |
| 181. #2185 | C2×C137 | semidirect |
| 182. #2020 | C2×C137 | semidirect |
| 183. #1350 | C2×C137 | semidirect |
| 184. #1349 | C2×C137 | semidirect |
| 185. #1315 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3203×C137 | 2 |
| #2188×C137 | 2 |
| #2185×C137 | 2 |
| #2020×C137 | 2 |
| #1350×C137 | 2 |
| #1349×C137 | 2 |
| #1315×C137 | 2 |
| #12113 | 137 |