Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
166 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 24. C32×C53 | Q8 | semidirect |
| 42. Dic106 | C32 | direct (N × H) |
| 71. C53 | Q8×C32 | semidirect |
| 82. C32 | Dic106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic106 | 2 |
| C4⋊#13133123 | 2 |
| #20272910 | 2 |
| C32×Dic53 | 2 |
| C4×C32×C53 | 2 |
| Q8×C32 | 53 |