Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 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×#13133803 | C2 | semidirect |
| 2. C2×C4×D428 | C2 | semidirect |
| 3. #20292819 | C2 | direct (N × H) |
| 4. C2×C4⋊(C107⋊C8) | C2 | semidirect |
| 5. C2×#16812030 | C2 | semidirect |
| 6. C2×#127×C107 | C2 | semidirect |
| 10. C2×#13133803 | C22 | semidirect |
| 13. C4×D428 | C22 | semidirect |
| 16. C4⋊(C107⋊C8) | C22 | semidirect |
| 17. #16812030 | C22 | semidirect |
| 22. #127×C107 | C22 | semidirect |
| 27. C2×D428 | D4 | semidirect |
| 67. C2×C4×C107 | D8 | semidirect |
| 78. D428 | C2×D4 | semidirect |
| 95. C4×C107 | C2×D8 | semidirect |
| 100. C2×C107 | #459 | semidirect |
| 106. C107 | C2×#459 | semidirect |
| 108. C2×#127 | D107 | semidirect |
| 122. #127 | C2×D107 | semidirect |
| 179. C2×C4 | #13133803 | semidirect |
| 202. C4 | C2×#13133803 | semidirect |
| 207. C2 | #20292819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133803 | 2 |
| C2×C4×D428 | 2 |
| #20292819 | 2 |
| C2×C4⋊(C107⋊C8) | 2 |
| C2×#16812030 | 2 |
| C2×#127×C107 | 2 |
| C2×#459 | 107 |