Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 18. Dic424 | C8 | semidirect |
| 59. #88322 | Q32 | semidirect |
| 87. C53 | C8×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic424 | 2 |
| #20273521 | 2 |
| #20272678 | 2 |
| C16×#88322 | 2 |
| C53×#1371 | 2 |
| C8×Q32 | 53 |