Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2286 conjugacy classes of subgroups; only the 947 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 947 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 |
|---|---|---|
| 10. C42×Dic53 | C4 | semidirect |
| 43. C42×C53 | C4⋊C4 | semidirect |
| 46. C4×Dic53 | C4⋊C4 | semidirect |
| 73. C4×C53 | #384 | semidirect |
| 75. Dic53 | #384 | semidirect |
| 94. C53 | #14692 | semidirect |
| 127. C42 | #11719919 | semidirect |
| 155. C4 | #16810492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810493 | 2 |
| C2×#16810492 | 2 |
| C2×C42×Dic53 | 2 |
| C2×C53×#384 | 2 |
| #14692 | 53 |