Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | #327 |
| commutator | C2×C8 | C2×C8×C53 |
| Frattini, cosocle | C2×#97 | C22×C53 |
| socle | C2×C53 | #1271 |
| prime radical | C23×C53 | #104 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C22×C4×C53 ◁ C2×#97×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #106×C53 | C8 | semidirect |
| 66. #7125 | C53 | direct (N × H) |
| 92. C53 | #7125 | direct (N × H) |
| 103. #106 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1946 | 2 |
| C53×#1375 | 2 |
| C53×#1281 | 2 |
| #7125 | 53 |