Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 25. #13133163 | C8 | direct (N × H) |
| 82. C8×C53 | Q32 | semidirect |
| 122. C53 | C8×Q32 | semidirect |
| 183. C8 | #13133163 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133163 | 2 |
| C8×Dic212 | 2 |
| #20272786 | 2 |
| #20272679 | 2 |
| #20272678 | 2 |
| C8×#11719908 | 2 |
| C8×Q16×C53 | 2 |
| C8×Q32 | 53 |