Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #386 |
| commutator | C22×C4 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C53×#3213 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#2980 | C2 | semidirect |
| 3. C53×#1553 | C2 | semidirect |
| 4. C53×#1533 | C2 | semidirect |
| 5. C53×#1469 | C2 | semidirect |
| 6. C53×#1308 | C2 | semidirect |
| 7. C53×#1287 | C2 | semidirect |
| 140. #9333 | C53 | direct (N × H) |
| 161. #2980 | C2×C53 | semidirect |
| 162. #1553 | C2×C53 | semidirect |
| 163. #1533 | C2×C53 | semidirect |
| 164. #1469 | C2×C53 | semidirect |
| 165. #1308 | C2×C53 | semidirect |
| 166. #1287 | C2×C53 | semidirect |
| 192. C53 | #9333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3213 | 2 |
| C53×#2980 | 2 |
| C53×#1553 | 2 |
| C53×#1533 | 2 |
| C53×#1469 | 2 |
| C53×#1308 | 2 |
| C53×#1287 | 2 |
| #9333 | 53 |