Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1470 conjugacy classes of subgroups; only the 480 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 480 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 |
|---|---|---|
| 1. C23×#11719910 | C2 | semidirect |
| 2. C2×#16811518 | C2 | direct (N × H) |
| 5. C22×#11719910 | C22 | semidirect |
| 6. #16811518 | C22 | direct (N × H) |
| 14. C2×#11719910 | C23 | semidirect |
| 34. C23×D53 | C16 | semidirect |
| 63. C22×D53 | C2×C16 | semidirect |
| 79. C22×C53 | C22⋊C16 | semidirect |
| 87. C2×D53 | C22×C16 | semidirect |
| 95. C2×C53 | C2×C22⋊C16 | semidirect |
| 109. C53 | C22×C22⋊C16 | semidirect |
| 179. C22 | #16811518 | direct (N × H) |
| 189. C2 | C2×#16811518 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719910 | 2 |
| C2×#16811518 | 2 |
| C23×C8×D53 | 2 |
| C22×C22⋊C16 | 53 |