Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D281 |
| commutator, socle, cosocle | C23×C281 | C24 |
| Fitting | #379×C281 | C2 |
| prime radical | C23×C22⋊D281 | C2 |
| hypercenter | #379 | D281 |
| hypocenter | C281 | #2405 |
| LCS | G ▷ C23×C281 ▷ C281 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#22582863 | C2 | semidirect |
| 3. C22×C22⋊Dic281 | C2 | semidirect |
| 4. #31823379 | C2 | semidirect |
| 5. #31823340 | C2 | semidirect |
| 6. #31823338 | C2 | semidirect |
| 7. #31823318 | C2 | semidirect |
| 8. #379×C281 | C2 | semidirect |
| 15. C23×Dic281 | C22 | semidirect |
| 16. C23×Dic281 | C22 | semidirect |
| 18. C2×C4⋊Dic281 | C22 | semidirect |
| 21. C2×C22⋊Dic281 | C22 | semidirect |
| 22. C2×#17985115 | C22 | semidirect |
| 23. C2×#17985115 | C22 | semidirect |
| 24. #22582786 | C22 | semidirect |
| 27. C2×C22⋊C4×C281 | C22 | semidirect |
| 28. C2×C22⋊C4×C281 | C22 | semidirect |
| 119. C22×C281 | #123 | semidirect |
| 142. C281 | #2405 | semidirect |
| 151. #379 | D281 | semidirect |
| 169. C2×C22⋊C4 | C2×D281 | semidirect |
| 170. C2×C22⋊C4 | C2×D281 | semidirect |
| 268. C22 | #22582863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D281 | 2 |
| C2×#22582863 | 2 |
| C22×C22⋊Dic281 | 2 |
| #31823379 | 2 |
| #31823340 | 2 |
| #31823338 | 2 |
| #31823318 | 2 |
| #379×C281 | 2 |
| #2405 | 281 |