Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1846 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1846 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20274630 | C2 | semidirect |
| 5. C23×D4×C53 | C4 | semidirect |
| 8. C22×C42×C53 | C4 | semidirect |
| 61. C2×C4×C53 | #99 | semidirect |
| 82. C23×D4 | Dic53 | semidirect |
| 85. C22×C42 | Dic53 | semidirect |
| 88. C53 | #8546 | semidirect |
| 142. C2×C4 | #13133132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274630 | 2 |
| C22×#127×C53 | 2 |
| #8546 | 53 |