Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
586 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C53 |
| Frattini, cosocle | C23×C4 | C23×C53 |
| prime radical | C24×C53 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C53×#391 | C4 | semidirect |
| 10. C53×#389 | C4 | semidirect |
| 122. #9153 | C53 | direct (N × H) |
| 159. #391 | C4×C53 | semidirect |
| 160. #389 | C4×C53 | semidirect |
| 171. C53 | #9153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2855 | 2 |
| C2×C53×#383 | 2 |
| C53×#1817 | 2 |
| C2×C53×#328 | 2 |
| C53×#1294 | 2 |
| #9153 | 53 |