Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1462 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1462 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C53 | C24 |
| commutator | C23 | C23×C4×C53 |
| Frattini, cosocle | C24 | C24×C53 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C4⋊Q8×C53 | C4 | semidirect |
| 64. #14663 | C53 | direct (N × H) |
| 85. C2×C4⋊Q8 | C4×C53 | semidirect |
| 92. C53 | #14663 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Q8×C53 | 2 |
| C2×C53×#383 | 2 |
| C53×#1446 | 2 |
| C53×#1445 | 2 |
| #14663 | 53 |