Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #124×C211 | C2 |
| hypercenter | #124 | D211 |
| hypocenter | C211 | #548 |
| LCS | G ▷ C22×C211 ▷ C211 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16809961 | C2 | semidirect |
| 2. C2×Q8×D211 | C2 | semidirect |
| 3. #20269963 | C2 | semidirect |
| 4. #20269954 | C2 | semidirect |
| 5. #20269953 | C2 | semidirect |
| 6. #20269950 | C2 | semidirect |
| 7. #20269948 | C2 | semidirect |
| 8. C4×Dic422 | C2 | semidirect |
| 9. C4×D844 | C2 | semidirect |
| 10. (C22⋊D211)⋊C4 | C2 | semidirect |
| 11. #124×C211 | C2 | semidirect |
| 40. Dic422 | D4 | semidirect |
| 68. C2×D211 | #41 | semidirect |
| 83. C211 | #548 | semidirect |
| 88. #124 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16809961 | 2 |
| C2×Q8×D211 | 2 |
| #20269963 | 2 |
| #20269954 | 2 |
| #20269953 | 2 |
| #20269950 | 2 |
| #20269948 | 2 |
| C4×Dic422 | 2 |
| C4×D844 | 2 |
| (C22⋊D211)⋊C4 | 2 |
| #124×C211 | 2 |
| #548 | 211 |