Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×#126 | C2 |
| prime radical | C23×C31 | C23 |
| hypercenter | #126 | D31 |
| hypocenter | C31 | #541 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11758467 | C2 | semidirect |
| 3. #11758466 | C2 | semidirect |
| 4. #11758466 | C2 | semidirect |
| 5. #11758466 | C2 | semidirect |
| 6. #11758465 | C2 | semidirect |
| 7. #11758464 | C2 | semidirect |
| 14. #11758447 | C2 | semidirect |
| 15. C4×Dic62 | C2 | semidirect |
| 107. C31 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#126 | 2 |
| #11758467 | 2 |
| #11758466 | 2 |
| #11758465 | 2 |
| #11758464 | 2 |
| #11758456 | 2 |
| #11758455 | 2 |
| #11758454 | 2 |
| #11758447 | 2 |
| C4×Dic62 | 2 |
| #541 | 31 |