Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 146 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 | #1893 |
| commutator | C2×C8 | C22×C4×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53×#3407 | C2 | semidirect |
| 3. C2×C53×#361 | C2 | semidirect |
| 4. C53×#1813 | C2 | semidirect |
| 5. C53×#1389 | C2 | semidirect |
| 40. M32×C53 | D4 | semidirect |
| 108. #13079 | C53 | direct (N × H) |
| 122. #3407 | C2×C53 | semidirect |
| 124. C2×#361 | C2×C53 | semidirect |
| 125. #1813 | C2×C53 | semidirect |
| 126. #1389 | C2×C53 | semidirect |
| 146. C53 | #13079 | direct (N × H) |
| 167. M32 | D4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3407 | 2 |
| C53×#3058 | 2 |
| C2×C53×#361 | 2 |
| C53×#1813 | 2 |
| C53×#1389 | 2 |
| #13079 | 53 |