Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2078 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 987 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D53 |
| commutator | C2×C53 | C2×C43 |
| Fitting | C2×C53×#376 | C2 |
| socle, prime radical, cosocle | C24×C53 | C24 |
| hypercenter | C2×#376 | D53 |
| hypocenter | C53 | #13750 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C4×C4⋊Dic53 | C4 | semidirect |
| 9. C53×#376 | C4 | semidirect |
| 32. C42×C53 | C42 | semidirect |
| 33. C4⋊Dic53 | C42 | semidirect |
| 70. #376 | Dic53 | semidirect |
| 73. C53 | #13750 | semidirect |
| 97. C42 | C4×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊Dic53 | 2 |
| #95×Dic53 | 2 |
| C2×C53×#376 | 2 |
| #13750 | 53 |