Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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×Q8×D107 | C2 | semidirect |
| 2. C22×#13133807 | C2 | semidirect |
| 3. C22×#13133805 | C2 | semidirect |
| 5. #20292767 | C2 | direct (N × H) |
| 6. C2×#16812032 | C2 | semidirect |
| 7. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 8. C2×#103×C107 | C2 | semidirect |
| 14. C2×Q8×D107 | C22 | semidirect |
| 20. C2×#13133807 | C22 | semidirect |
| 22. C2×#13133805 | C22 | semidirect |
| 27. #16812032 | C22 | semidirect |
| 28. (C2×D107)⋊C8 | C22 | semidirect |
| 32. #103×C107 | C22 | semidirect |
| 39. C2×Dic214 | D4 | semidirect |
| 65. C2×Q8×C107 | D4 | semidirect |
| 81. C22×D107 | SD16 | semidirect |
| 85. Q8×C107 | C2×D4 | semidirect |
| 109. Dic214 | C2×D4 | semidirect |
| 123. C2×D107 | C2×SD16 | semidirect |
| 131. C2×C107 | #448 | semidirect |
| 138. C107 | C2×#448 | semidirect |
| 145. C2×#103 | D107 | semidirect |
| 169. #103 | C2×D107 | semidirect |
| 184. C2×Q8 | D428 | semidirect |
| 227. Q8 | C2×D428 | semidirect |
| 271. C2 | #20292767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D107 | 2 |
| C22×#13133807 | 2 |
| C22×#13133805 | 2 |
| C2×#16812084 | 2 |
| #20292767 | 2 |
| C2×#16812032 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C2×#103×C107 | 2 |
| C2×#448 | 107 |