Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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×D211 |
| commutator, socle, cosocle | C22×C211 | C24 |
| Fitting | C22×D4×C211 | C2 |
| hypercenter | C22×D4 | D211 |
| hypocenter | C211 | #535 |
| LCS | G ▷ C22×C211 ▷ C211 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16809962 | C2 | semidirect |
| 2. #20269973 | C2 | semidirect |
| 3. #20269964 | C2 | semidirect |
| 4. #20269948 | C2 | semidirect |
| 5. #20269946 | C2 | semidirect |
| 6. #20269936 | C2 | semidirect |
| 7. C22×D4×C211 | C2 | semidirect |
| 9. C2×Dic422 | C22 | semidirect |
| 10. C2×D844 | C22 | semidirect |
| 12. C2×C22⋊D211 | C22 | semidirect |
| 13. C2×C4×D211 | C22 | semidirect |
| 14. C4⋊Dic211 | C22 | semidirect |
| 16. C22⋊Dic211 | C22 | semidirect |
| 17. C4×Dic211 | C22 | semidirect |
| 37. C2×C4×C211 | D4 | semidirect |
| 57. C211 | #535 | semidirect |
| 60. C22×D4 | D211 | semidirect |
| 95. C2×C4 | C22⋊D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16809962 | 2 |
| #20269973 | 2 |
| #20269964 | 2 |
| #20269948 | 2 |
| #20269946 | 2 |
| #20269936 | 2 |
| C22×D4×C211 | 2 |
| #535 | 211 |