Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #6157 |
| commutator, hypocenter | C53 | C2×C4×C32 |
| Frattini | C16 | C22×#6157 |
| Fitting | C2×C32×C53 | C4 |
| socle | C22×C53 | C4×C16 |
| prime radical | C22×D53 | C2×C16 |
| cosocle | C16×D53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×#6157 | C2 | direct (N × H) |
| 7. D53⋊C32 | C4 | semidirect |
| 9. C2×#13133267 | C4 | semidirect |
| 13. C2×#13133123 | C4 | semidirect |
| 14. C32×D53 | C4 | semidirect |
| 16. C2×C32×C53 | C4 | semidirect |
| 24. #13133267 | C2×C4 | semidirect |
| 31. #13133123 | C2×C4 | semidirect |
| 33. C32×C53 | C2×C4 | semidirect |
| 53. C2×#6157 | C32 | direct (N × H) |
| 71. #6157 | C2×C32 | direct (N × H) |
| 80. C2×C53 | C4×C32 | semidirect |
| 82. D53 | C4×C32 | semidirect |
| 93. C2×C32 | #6157 | direct (N × H) |
| 96. C53 | C2×C4×C32 | semidirect |
| 113. C32 | C2×#6157 | direct (N × H) |
| 157. C2 | C32×#6157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊C32 | 2 |
| C2×C16×#6157 | 2 |
| C32×#6157 | 2 |
| C2×C32×D53 | 2 |
| C2×C4×C32 | 53 |