Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 574 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 | #394 |
| commutator, Frattini, cosocle | C23×C4 | C23×C53 |
| prime radical | C53×#3186 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1964 | C2 | semidirect |
| 3. C53×#1893 | C2 | semidirect |
| 4. C53×#1850 | C2 | semidirect |
| 5. C53×#1289 | C2 | semidirect |
| 96. C22⋊C4×C53 | D8 | semidirect |
| 142. #10564 | C53 | direct (N × H) |
| 169. #1964 | C2×C53 | semidirect |
| 170. #1893 | C2×C53 | semidirect |
| 171. #1850 | C2×C53 | semidirect |
| 172. #1289 | C2×C53 | semidirect |
| 196. C53 | #10564 | direct (N × H) |
| 272. C22⋊C4 | D8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3186 | 2 |
| C53×#1964 | 2 |
| C53×#1893 | 2 |
| C53×#1850 | 2 |
| C53×#1289 | 2 |
| #10564 | 53 |