Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#466 | C22 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C53×#424 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#2236 | C2 | semidirect |
| 4. C53×#2089 | C2 | semidirect |
| 5. C53×#1350 | C2 | semidirect |
| 7. C53×#1323 | C2 | semidirect |
| 121. #12297 | C53 | direct (N × H) |
| 139. #2236 | C2×C53 | semidirect |
| 141. #2089 | C2×C53 | semidirect |
| 142. #1350 | C2×C53 | semidirect |
| 144. #1323 | C2×C53 | semidirect |
| 169. C53 | #12297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3262 | 2 |
| C53×#2236 | 2 |
| C53×#2232 | 2 |
| C53×#2089 | 2 |
| C53×#1350 | 2 |
| C53×#1349 | 2 |
| C53×#1323 | 2 |
| #12297 | 53 |