Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2046 conjugacy classes of subgroups; only the 1659 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1659 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×C43 | D53 |
| commutator, hypocenter | C53 | C2×C42×C8 |
| Frattini | C22×C4 | C23×D53 |
| Fitting | C2×C43×C53 | C2 |
| socle, prime radical | C24×C53 | C22×C4 |
| cosocle | C22×C4×C53 | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×#88322 | C2 | direct (N × H) |
| 5. C2×C4×#88322 | C4 | direct (N × H) |
| 13. C4×#88322 | C2×C4 | direct (N × H) |
| 16. C2×C42×C53 | C8 | semidirect |
| 29. C42×C53 | C2×C8 | semidirect |
| 31. C2×#88322 | C42 | direct (N × H) |
| 36. C2×C4×C53 | C4×C8 | semidirect |
| 42. #88322 | C2×C42 | direct (N × H) |
| 49. C4×C53 | C2×C4×C8 | semidirect |
| 54. C2×C53 | C42×C8 | semidirect |
| 64. C53 | C2×C42×C8 | semidirect |
| 69. C2×C42 | #88322 | direct (N × H) |
| 84. C42 | C2×#88322 | direct (N × H) |
| 90. C2×C4 | C4×#88322 | direct (N × H) |
| 102. C4 | C2×C4×#88322 | direct (N × H) |
| 104. C2 | C42×#88322 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#88322 | 2 |
| C42×#88322 | 2 |
| C2×C43×C53 | 2 |
| C2×C42×C8 | 53 |