Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C22×D16×C53 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ C2×C4×C8×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C53×C4⋊C16 | C2 | semidirect |
| 3. C2×C53×#357 | C2 | semidirect |
| 4. C53×#1970 | C2 | semidirect |
| 5. C53×#1380 | C2 | semidirect |
| 88. C2×C4×C53 | D16 | semidirect |
| 97. #13448 | C53 | direct (N × H) |
| 117. C2×C4⋊C16 | C2×C53 | semidirect |
| 118. C2×#357 | C2×C53 | semidirect |
| 119. #1970 | C2×C53 | semidirect |
| 120. #1380 | C2×C53 | semidirect |
| 138. C53 | #13448 | direct (N × H) |
| 210. C2×C4 | D16×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D16×C53 | 2 |
| C2×C53×C4⋊C16 | 2 |
| C2×C53×#357 | 2 |
| C53×#1970 | 2 |
| C53×#1380 | 2 |
| #13448 | 53 |