Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1014 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 318 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, Frattini, cosocle | C24 | C24×C53 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 74. #17307 | C53 | direct (N × H) |
| 104. C53 | #17307 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1444 | 2 |
| C53×#1442 | 2 |
| C53×#1441 | 2 |
| #17307 | 53 |