Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 203 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. C22×#13133160 | C2 | semidirect |
| 3. C2×#16811008 | C2 | semidirect |
| 4. #20276977 | C2 | direct (N × H) |
| 5. C2×C16×Dic53 | C2 | semidirect |
| 6. C22×Q32×C53 | C2 | semidirect |
| 11. C2×#13133160 | C22 | semidirect |
| 16. #16811008 | C22 | semidirect |
| 18. C16×Dic53 | C22 | semidirect |
| 21. C2×Q32×C53 | C22 | semidirect |
| 114. C22×Q32 | D53 | semidirect |
| 120. C2×C53 | #2249 | semidirect |
| 129. C2×Q32 | C2×D53 | semidirect |
| 140. C53 | C2×#2249 | semidirect |
| 232. C2 | #20276977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133160 | 2 |
| C22×D848 | 2 |
| C2×#16811008 | 2 |
| #20276977 | 2 |
| C2×C16×Dic53 | 2 |
| C22×Q32×C53 | 2 |
| C2×#2249 | 53 |