Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 2. #20276996 | C2 | direct (N × H) |
| 27. C2×#11719908 | Q8 | semidirect |
| 36. C2×C16×C53 | Q8 | semidirect |
| 59. C16×C53 | C2×Q8 | semidirect |
| 60. #11719908 | C2×Q8 | semidirect |
| 93. C2×C53 | #2254 | semidirect |
| 109. C53 | C2×#2254 | semidirect |
| 121. C2×C16 | Dic106 | semidirect |
| 150. C16 | C2×Dic106 | semidirect |
| 176. C2 | #20276996 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811027 | 2 |
| #20276996 | 2 |
| C2×#16810451 | 2 |
| C2×#16810450 | 2 |
| C2×C16×Dic53 | 2 |
| C2×C53×#367 | 2 |
| C2×#2254 | 53 |