Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #121×C211 | C2 |
| hypercenter | #121 | D211 |
| hypocenter | C211 | #538 |
| LCS | G ▷ C22×C211 ▷ C211 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20269972 | C2 | semidirect |
| 2. #20269963 | C2 | semidirect |
| 3. #20269961 | C2 | semidirect |
| 4. #20269956 | C2 | semidirect |
| 5. #20269949 | C2 | semidirect |
| 6. #20269945 | C2 | semidirect |
| 7. D4×Dic211 | C2 | semidirect |
| 8. C2×(C2×D211)⋊C4 | C2 | semidirect |
| 9. #121×C211 | C2 | semidirect |
| 11. C2×Dic422 | C22 | semidirect |
| 15. C22×Dic211 | C22 | semidirect |
| 16. C4⋊Dic211 | C22 | semidirect |
| 17. C4⋊Dic211 | C22 | semidirect |
| 18. Dic211⋊C4 | C22 | semidirect |
| 20. C22⋊Dic211 | C22 | semidirect |
| 25. C4×Dic211 | C22 | semidirect |
| 27. C2×D4×C211 | C22 | semidirect |
| 29. C4⋊C4×C211 | C22 | semidirect |
| 30. C22⋊C4×C211 | C22 | semidirect |
| 74. C211 | #538 | semidirect |
| 81. #121 | D211 | semidirect |
| 90. C2×D4 | C2×D211 | semidirect |
| 97. C4⋊C4 | C2×D211 | semidirect |
| 104. C22⋊C4 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20269972 | 2 |
| #20269963 | 2 |
| #20269961 | 2 |
| #20269956 | 2 |
| #20269949 | 2 |
| #20269945 | 2 |
| D4×Dic211 | 2 |
| C2×(C2×D211)⋊C4 | 2 |
| #121×C211 | 2 |
| #538 | 211 |