Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4×Dic214 | C2 | semidirect |
| 4. C4×#13133807 | C2 | direct (N × H) |
| 5. C2×#16812041 | C2 | semidirect |
| 6. C2×#16812034 | C2 | semidirect |
| 8. C2×C4×C8×C107 | C2 | semidirect |
| 12. C2×#13133807 | C4 | direct (N × H) |
| 15. C4×Dic214 | C22 | semidirect |
| 23. #16812041 | C22 | semidirect |
| 24. #16812034 | C22 | semidirect |
| 29. C4×C8×C107 | C22 | semidirect |
| 33. C2×Dic214 | C2×C4 | semidirect |
| 44. #13133807 | C2×C4 | direct (N × H) |
| 56. C2×C8×C107 | C2×C4 | semidirect |
| 67. C2×C4×C107 | SD16 | semidirect |
| 86. Dic214 | C22×C4 | semidirect |
| 88. C8×C107 | C22×C4 | semidirect |
| 99. C4×C107 | C2×SD16 | semidirect |
| 105. C2×C107 | C4×SD16 | semidirect |
| 111. C107 | C2×C4×SD16 | semidirect |
| 119. C2×C4×C8 | D107 | semidirect |
| 140. C4×C8 | C2×D107 | semidirect |
| 160. C2×C8 | C4×D107 | semidirect |
| 191. C2×C4 | #13133807 | direct (N × H) |
| 199. C8 | C2×C4×D107 | semidirect |
| 213. C4 | C2×#13133807 | direct (N × H) |
| 217. C2 | C4×#13133807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| C2×C4×Dic214 | 2 |
| C2×C4×D428 | 2 |
| C4×#13133807 | 2 |
| C2×#16812041 | 2 |
| C2×#16812034 | 2 |
| C2×#16812031 | 2 |
| C2×C4×C8×C107 | 2 |
| C2×C4×SD16 | 107 |