Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | #486 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| socle | C2×C53 | #2041 |
| prime radical | C53×#3150 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C22×C4×C53 ◁ C2×#97×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#2148 | C2 | semidirect |
| 3. C53×#2145 | C2 | semidirect |
| 4. C53×#1946 | C2 | semidirect |
| 5. C53×#1375 | C2 | semidirect |
| 48. #106×C53 | D4 | semidirect |
| 114. #13416 | C53 | direct (N × H) |
| 129. #2148 | C2×C53 | semidirect |
| 130. #2145 | C2×C53 | semidirect |
| 131. #1946 | C2×C53 | semidirect |
| 132. #1375 | C2×C53 | semidirect |
| 152. C53 | #13416 | direct (N × H) |
| 181. #106 | D4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3150 | 2 |
| C53×#2148 | 2 |
| C53×#2145 | 2 |
| C53×#1946 | 2 |
| C53×#1375 | 2 |
| #13416 | 53 |