Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #1514 |
| commutator | C2×C8 | C22×C4×C53 |
| Frattini, cosocle | C2×M16 | C23×C53 |
| prime radical | C53×#469 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C4×M16×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#2165 | C2 | semidirect |
| 3. C53×#1841 | C2 | semidirect |
| 4. C53×#1342 | C2 | semidirect |
| 6. C53×#1340 | C2 | semidirect |
| 9. C53×#499 | C4 | semidirect |
| 10. C53×#495 | C4 | semidirect |
| 15. C53×#442 | C4 | semidirect |
| 16. C53×#441 | C4 | semidirect |
| 120. #11836 | C53 | direct (N × H) |
| 137. #2165 | C2×C53 | semidirect |
| 138. #1841 | C2×C53 | semidirect |
| 139. #1342 | C2×C53 | semidirect |
| 141. #1340 | C2×C53 | semidirect |
| 148. #499 | C4×C53 | semidirect |
| 149. #495 | C4×C53 | semidirect |
| 154. #442 | C4×C53 | semidirect |
| 155. #441 | C4×C53 | semidirect |
| 166. C53 | #11836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3183 | 2 |
| C53×#2165 | 2 |
| C53×#1841 | 2 |
| C53×#1342 | 2 |
| C53×#1341 | 2 |
| C53×#1340 | 2 |
| C53×#1339 | 2 |
| #11836 | 53 |