Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C2×#41×C53 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C53×#367 | C2 | semidirect |
| 4. C53×#1387 | C2 | semidirect |
| 5. C53×#1381 | C2 | semidirect |
| 77. #13496 | C53 | direct (N × H) |
| 88. C2×#367 | C2×C53 | semidirect |
| 91. #1387 | C2×C53 | semidirect |
| 92. #1381 | C2×C53 | semidirect |
| 106. C53 | #13496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#367 | 2 |
| C53×#2113 | 2 |
| C53×#1816 | 2 |
| C53×#1387 | 2 |
| C53×#1381 | 2 |
| #13496 | 53 |