Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
30862 conjugacy classes of subgroups; only the 1374 normal subgroups are shown.
This group has 30862 conjugacy classes of subgroups — too many to draw. Only its 1374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C53 | C24 |
| commutator | C23 | C23×C4×C53 |
| Frattini, cosocle | C24 | C24×C53 |
| prime radical | C27×C53 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C53×#379 | C2 | semidirect |
| 4. C26×C53 | C4 | semidirect |
| 6. C22×C22⋊C4×C53 | C22 | semidirect |
| 14. C23×C4×C53 | C23 | semidirect |
| 22. C24×C53 | C22⋊C4 | semidirect |
| 39. #14679 | C53 | direct (N × H) |
| 43. C22×C53 | #379 | semidirect |
| 48. C2×#379 | C2×C53 | semidirect |
| 53. C26 | C4×C53 | semidirect |
| 55. C22×C22⋊C4 | C22×C53 | semidirect |
| 57. C53 | #14679 | direct (N × H) |
| 64. C23×C4 | C23×C53 | semidirect |
| 72. C24 | C22⋊C4×C53 | semidirect |
| 92. C22 | C53×#379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×C53 | 2 |
| C2×C53×#379 | 2 |
| #14679 | 53 |