Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×D313 |
| commutator, socle, cosocle | C22×C313 | C24 |
| Fitting | #124×C313 | C2 |
| prime radical | C2×#19097560 | C2 |
| hypercenter | #124 | D313 |
| hypocenter | C313 | #536 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D313 | C2 | semidirect |
| 3. #23756497 | C2 | semidirect |
| 4. #23756495 | C2 | semidirect |
| 5. #23756484 | C2 | semidirect |
| 6. #23756479 | C2 | semidirect |
| 7. #23756474 | C2 | semidirect |
| 8. #23756454 | C2 | semidirect |
| 9. #124×C313 | C2 | semidirect |
| 63. C313 | #536 | semidirect |
| 70. #124 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097560 | 2 |
| C2×Q8×D313 | 2 |
| #23756497 | 2 |
| #23756495 | 2 |
| #23756484 | 2 |
| #23756479 | 2 |
| #23756474 | 2 |
| #23756454 | 2 |
| #124×C313 | 2 |
| #536 | 313 |