Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
266 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C53 | #95 |
| commutator | C2×C4 | C4×C8×C53 |
| Frattini, cosocle | C2×C4×C8 | C22×C53 |
| socle | C22×C53 | #336 |
| prime radical | C23×C53 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C53 ◁ C2×C4×C8×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C53×C4⋊C16 | C4 | semidirect |
| 56. #7149 | C53 | direct (N × H) |
| 78. C4⋊C16 | C4×C53 | semidirect |
| 81. C53 | #7149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2163 | 2 |
| C4×#97×C53 | 2 |
| #7149 | 53 |