Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 267 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. #20276997 | C2 | direct (N × H) |
| 25. C2×C16×C53 | Q8 | semidirect |
| 44. C16×C53 | C2×Q8 | semidirect |
| 71. C2×C53 | #2254 | semidirect |
| 83. C53 | C2×#2254 | semidirect |
| 92. C2×C16 | Dic106 | semidirect |
| 114. C16 | C2×Dic106 | semidirect |
| 136. C2 | #20276997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811028 | 2 |
| #20276997 | 2 |
| C2×#16810451 | 2 |
| C2×C4×C16×C53 | 2 |
| C2×#2254 | 53 |