Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2414 conjugacy classes of subgroups; only the 278 normal subgroups are shown.
This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 278 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#95 |
| commutator | C23 | C2×C42×C53 |
| Frattini, cosocle | C25 | C23×C53 |
| prime radical | C26×C53 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C26×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1304 | C2 | semidirect |
| 5. C22×C22⋊C4×C53 | C4 | semidirect |
| 7. C53×#379 | C4 | semidirect |
| 21. C2×C22⋊C4×C53 | C2×C4 | semidirect |
| 83. #8101 | C53 | direct (N × H) |
| 106. #1304 | C2×C53 | semidirect |
| 115. C22×C22⋊C4 | C4×C53 | semidirect |
| 117. #379 | C4×C53 | semidirect |
| 119. C53 | #8101 | direct (N × H) |
| 132. C2×C22⋊C4 | C2×C4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#379 | 2 |
| C53×#1304 | 2 |
| #8101 | 53 |