Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D53 |
| commutator, hypocenter | C53 | C2×C4×C32 |
| Frattini | C2×C16 | C22×D53 |
| Fitting | C22×C32×C53 | C2 |
| socle, prime radical | C23×C53 | C2×C16 |
| cosocle | C2×C16×C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×Dic53 | C2 | direct (N × H) |
| 7. C2×#13133123 | C4 | semidirect |
| 12. C2×C32×C53 | C4 | semidirect |
| 20. #13133123 | C2×C4 | semidirect |
| 26. C32×C53 | C2×C4 | semidirect |
| 46. C2×Dic53 | C32 | direct (N × H) |
| 59. Dic53 | C2×C32 | direct (N × H) |
| 64. C2×C53 | C4×C32 | semidirect |
| 72. C2×C32 | Dic53 | direct (N × H) |
| 76. C53 | C2×C4×C32 | semidirect |
| 89. C32 | C2×Dic53 | direct (N × H) |
| 122. C2 | C32×Dic53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133123 | 2 |
| C2×C16×Dic53 | 2 |
| C32×Dic53 | 2 |
| C22×C32×C53 | 2 |
| C2×C4×C32 | 53 |