Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2502 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 2502 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 | C24×C53 | C24 |
| commutator | C23 | C23×C4×C53 |
| Frattini, cosocle | C24 | C24×C53 |
| prime radical | C22×#127×C53 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C53×#383 | C2 | semidirect |
| 3. C53×#1438 | C2 | semidirect |
| 6. C2×#127×C53 | C4 | semidirect |
| 35. C42×C53 | C22⋊C4 | semidirect |
| 50. #14661 | C53 | direct (N × H) |
| 61. C2×#383 | C2×C53 | semidirect |
| 62. #1438 | C2×C53 | semidirect |
| 69. C2×#127 | C4×C53 | semidirect |
| 74. C53 | #14661 | direct (N × H) |
| 99. C42 | C22⋊C4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#127×C53 | 2 |
| C2×C53×#383 | 2 |
| C53×#1438 | 2 |
| #14661 | 53 |