Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C53 | C22⋊C4 |
| commutator | C2×C4 | C22×C8×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| socle | C22×C53 | C2×C22⋊C8 |
| prime radical | C2×#41×C53 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C53 ◁ C2×C4×C8×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#2162 | C2 | semidirect |
| 3. C53×#1323 | C2 | semidirect |
| 86. #11462 | C53 | direct (N × H) |
| 100. #2162 | C2×C53 | semidirect |
| 101. #1323 | C2×C53 | semidirect |
| 119. C53 | #11462 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2922 | 2 |
| C53×#2162 | 2 |
| C53×#1323 | 2 |
| C53×#1315 | 2 |
| #11462 | 53 |