Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 522 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, socle | C23×C53 | #95 |
| commutator | C2×C4 | C4×C8×C53 |
| Frattini, cosocle | C22×C42 | C22×C53 |
| prime radical | C24×C53 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C53×#336 | C4 | semidirect |
| 17. C2×C42×C53 | C8 | semidirect |
| 80. #7017 | C53 | direct (N × H) |
| 113. #336 | C4×C53 | semidirect |
| 114. C53 | #7017 | direct (N × H) |
| 123. C2×C42 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1817 | 2 |
| C4×#95×C53 | 2 |
| #7017 | 53 |