Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 462 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 | C26×C53 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C53×#1439 | C2 | semidirect |
| 5. C22×C4⋊C4×C53 | C22 | semidirect |
| 9. C53×#379 | C4 | semidirect |
| 10. C2×#95×C53 | C22 | semidirect |
| 37. C24×C53 | C4⋊C4 | semidirect |
| 79. #14673 | C53 | direct (N × H) |
| 99. #1439 | C2×C53 | semidirect |
| 107. C22×C4⋊C4 | C22×C53 | semidirect |
| 111. #379 | C4×C53 | semidirect |
| 112. C2×#95 | C22×C53 | semidirect |
| 113. C53 | #14673 | direct (N × H) |
| 140. C24 | C4⋊C4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#379 | 2 |
| C53×#1439 | 2 |
| #14673 | 53 |