Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
1072 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| prime radical | #3549×C137 | C2 |
| LCS | G ▷ 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. #3152×C137 | C2 | semidirect |
| 3. #3141×C137 | C2 | semidirect |
| 4. #1659×C137 | C2 | semidirect |
| 5. #1525×C137 | C2 | semidirect |
| 6. #1525×C137 | C2 | semidirect |
| 17. C2×C4⋊Q8×C137 | C22 | semidirect |
| 18. #497×C137 | C22 | semidirect |
| 21. #489×C137 | C22 | semidirect |
| 25. C4×M16×C137 | C22 | semidirect |
| 26. C4×M16×C137 | C22 | semidirect |
| 27. #329×C137 | C22 | semidirect |
| 28. #329×C137 | C22 | semidirect |
| 170. #19074 | C137 | direct (N × H) |
| 171. C137 | #19074 | direct (N × H) |
| 173. #3152 | C2×C137 | semidirect |
| 174. #3141 | C2×C137 | semidirect |
| 175. #1659 | C2×C137 | semidirect |
| 176. #1525 | C2×C137 | semidirect |
| 177. #1525 | C2×C137 | semidirect |
| 188. C2×C4⋊Q8 | C22×C137 | semidirect |
| 189. #497 | C22×C137 | semidirect |
| 192. #489 | C22×C137 | semidirect |
| 196. C4×M16 | C22×C137 | semidirect |
| 197. C4×M16 | C22×C137 | semidirect |
| 198. #329 | C22×C137 | semidirect |
| 199. #329 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3549×C137 | 2 |
| #3152×C137 | 2 |
| #3141×C137 | 2 |
| #1659×C137 | 2 |
| #1525×C137 | 2 |
| #19074 | 137 |