Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 422 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 |
| 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 |
|---|---|---|
| 1. #3203×C137 | C2 | semidirect |
| 2. #2187×C137 | C2 | semidirect |
| 3. #2184×C137 | C2 | semidirect |
| 4. #2018×C137 | C2 | semidirect |
| 5. #1350×C137 | C2 | semidirect |
| 6. #1349×C137 | C2 | semidirect |
| 7. #1315×C137 | C2 | semidirect |
| 184. #12110 | C137 | direct (N × H) |
| 185. C137 | #12110 | direct (N × H) |
| 186. #3203 | C2×C137 | semidirect |
| 187. #2187 | C2×C137 | semidirect |
| 188. #2184 | C2×C137 | semidirect |
| 189. #2018 | C2×C137 | semidirect |
| 190. #1350 | C2×C137 | semidirect |
| 191. #1349 | C2×C137 | semidirect |
| 192. #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 |
| #2187×C137 | 2 |
| #2184×C137 | 2 |
| #2018×C137 | 2 |
| #1350×C137 | 2 |
| #1349×C137 | 2 |
| #1315×C137 | 2 |
| #12110 | 137 |