Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #1316 |
| commutator | C24 | C2×C8×C53 |
| Frattini, cosocle | #407 | C22×C53 |
| prime radical | C23×D4×C53 | C4 |
| LCS | G ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C22×C4×C53 ◁ C53×#407 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1320 | C2 | semidirect |
| 71. #7340 | C53 | direct (N × H) |
| 90. #1320 | C2×C53 | semidirect |
| 101. C53 | #7340 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1783 | 2 |
| C53×#1320 | 2 |
| #7340 | 53 |