Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
878 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 3. #20274333 | C2 | direct (N × H) |
| 37. C2×C8×C53 | Q16 | semidirect |
| 58. C8×C53 | C2×Q16 | semidirect |
| 72. C2×C53 | #1713 | semidirect |
| 85. C53 | C2×#1713 | semidirect |
| 109. C2×C8 | Dic212 | semidirect |
| 129. C8 | C2×Dic212 | semidirect |
| 138. C2 | #20274333 | 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 |
| C2×#16811003 | 2 |
| #20274333 | 2 |
| C2×C82×C53 | 2 |
| C2×#1713 | 53 |