Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 142 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 | C2×#99 |
| commutator | C2×C4 | C22×C8×C53 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C53 |
| prime radical | C23×D4×C53 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#117×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1458 | C2 | semidirect |
| 3. C53×#1318 | C2 | semidirect |
| 12. C53×#324 | C22 | semidirect |
| 19. C22×D4×C53 | C8 | semidirect |
| 108. #11433 | C53 | direct (N × H) |
| 132. #1458 | C2×C53 | semidirect |
| 133. #1318 | C2×C53 | semidirect |
| 149. #324 | C22×C53 | semidirect |
| 151. C53 | #11433 | direct (N × H) |
| 157. C22×D4 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2309 | 2 |
| C53×#1458 | 2 |
| C53×#1318 | 2 |
| #11433 | 53 |