Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 226 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 | C22×C53 | #354 |
| commutator | C2×C42 | C2×C4×C53 |
| Frattini, cosocle | #390 | C22×C53 |
| prime radical | C22×D4×C53 | D4 |
| LCS | G ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C53 ◁ C22×C4×C53 ◁ C53×#390 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#125×C53 | C4 | semidirect |
| 9. C53×#336 | C4 | semidirect |
| 75. #7428 | C53 | direct (N × H) |
| 104. C2×#125 | C4×C53 | semidirect |
| 109. #336 | C4×C53 | semidirect |
| 111. C53 | #7428 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2025 | 2 |
| C53×#1393 | 2 |
| C53×#1318 | 2 |
| #7428 | 53 |