Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
726 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20272644 | C2 | direct (N × H) |
| 27. C23×Dic53 | C8 | semidirect |
| 90. C22×Dic53 | C2×C8 | semidirect |
| 202. C2×C53 | #1317 | semidirect |
| 221. C53 | C2×#1317 | semidirect |
| 399. C2 | #20272644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810484 | 2 |
| C2×#16810347 | 2 |
| #20272644 | 2 |
| C2×C53×#323 | 2 |
| C2×#1317 | 53 |