Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1350 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 459 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. C42×D212 | C2 | semidirect |
| 3. C4×#13133151 | C2 | semidirect |
| 4. C4×#13133139 | C2 | semidirect |
| 5. C42×C8×C53 | C2 | semidirect |
| 9. C4×D424 | C4 | direct (N × H) |
| 22. C4×D212 | C2×C4 | semidirect |
| 27. #13133151 | C2×C4 | semidirect |
| 28. #13133139 | C2×C4 | semidirect |
| 36. C4×C8×C53 | C2×C4 | semidirect |
| 51. C42×C53 | D8 | semidirect |
| 58. D424 | C42 | direct (N × H) |
| 74. D212 | C2×C42 | semidirect |
| 77. C8×C53 | C2×C42 | semidirect |
| 86. C4×C53 | C4×D8 | semidirect |
| 94. C42×C8 | D53 | semidirect |
| 111. C53 | C42×D8 | semidirect |
| 129. C4×C8 | C4×D53 | semidirect |
| 150. C42 | D424 | direct (N × H) |
| 171. C8 | C42×D53 | semidirect |
| 180. C4 | C4×D424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D424 | 2 |
| C42×D212 | 2 |
| C4×#13133151 | 2 |
| C4×#13133139 | 2 |
| C42×C8×C53 | 2 |
| C42×D8 | 53 |