Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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. #20293024 | C2 | semidirect |
| 3. #20292450 | C2 | semidirect |
| 4. #20292449 | C2 | semidirect |
| 5. #20292447 | C2 | semidirect |
| 29. Q16×C107 | Q8 | semidirect |
| 31. D8×C107 | Q8 | semidirect |
| 61. C107 | #2230 | semidirect |
| 82. Q16 | Dic214 | semidirect |
| 84. D8 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293024 | 2 |
| #20292744 | 2 |
| #20292450 | 2 |
| #20292449 | 2 |
| #20292447 | 2 |
| #20292437 | 2 |
| #360×C107 | 2 |
| #2230 | 107 |