Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 364 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, socle | C2×C53 | #1519 |
| commutator | C2×C8 | C22×C4×C53 |
| Frattini, cosocle | C2×M16 | C23×C53 |
| prime radical | C2×#41×C53 | D4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C2×#131×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C53×#1340 | C2 | semidirect |
| 5. C22×Q16×C53 | C4 | semidirect |
| 9. C53×#470 | C4 | semidirect |
| 14. C53×#427 | C4 | semidirect |
| 123. #11869 | C53 | direct (N × H) |
| 142. #1340 | C2×C53 | semidirect |
| 148. C22×Q16 | C4×C53 | semidirect |
| 152. #470 | C4×C53 | semidirect |
| 157. #427 | C4×C53 | semidirect |
| 163. C53 | #11869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3059 | 2 |
| C53×#2115 | 2 |
| C53×#1812 | 2 |
| C53×#1340 | 2 |
| #11869 | 53 |