Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
228 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| socle | C2×C53 | #2085 |
| prime radical | C23×C53 | #137 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C22×C4×C53 ◁ C53×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 89. #13513 | C53 | direct (N × H) |
| 124. C53 | #13513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#368 | 2 |
| C53×#2155 | 2 |
| C53×#1953 | 2 |
| C53×#1833 | 2 |
| C53×#1388 | 2 |
| C53×#1382 | 2 |
| C53×#1379 | 2 |
| #13513 | 53 |