Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 339 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×C82 | D53 |
| commutator, hypocenter | C53 | C2×C8×C16 |
| Frattini | C4×C8 | C22×D53 |
| Fitting | C2×C82×C53 | C2 |
| socle, prime radical | C23×C53 | C4×C8 |
| cosocle | C4×C8×C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×#11719908 | C2 | direct (N × H) |
| 11. C2×#11719908 | C8 | direct (N × H) |
| 23. C2×C8×C53 | C16 | semidirect |
| 31. #11719908 | C2×C8 | direct (N × H) |
| 40. C8×C53 | C2×C16 | semidirect |
| 53. C2×C53 | C8×C16 | semidirect |
| 63. C53 | C2×C8×C16 | semidirect |
| 76. C2×C8 | #11719908 | direct (N × H) |
| 93. C8 | C2×#11719908 | direct (N × H) |
| 102. C2 | C8×#11719908 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719908 | 2 |
| C8×#11719908 | 2 |
| C2×C82×C53 | 2 |
| C2×C8×C16 | 53 |