Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16810453 | C2 | semidirect |
| 3. #20272900 | C2 | direct (N × H) |
| 4. C22×C32×C53 | C2 | semidirect |
| 15. #16810453 | C22 | semidirect |
| 19. C2×C32×C53 | C22 | semidirect |
| 108. C22×C32 | D53 | semidirect |
| 113. C2×C53 | #1417 | semidirect |
| 128. C2×C32 | C2×D53 | semidirect |
| 131. C53 | C2×#1417 | semidirect |
| 221. C2 | #20272900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| C2×#16810453 | 2 |
| #20272900 | 2 |
| C22×C32×C53 | 2 |
| C2×#1417 | 53 |