Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20293178 | C2 | semidirect |
| 2. #20293004 | C2 | semidirect |
| 3. #20292975 | C2 | semidirect |
| 4. #20292864 | C2 | semidirect |
| 5. #20292709 | C2 | semidirect |
| 6. C4×C8×D107 | C2 | semidirect |
| 7. #500×C107 | C2 | semidirect |
| 63. C4×D107 | D8 | semidirect |
| 64. C8×C107 | #41 | semidirect |
| 86. C107 | #3169 | semidirect |
| 88. #500 | D107 | semidirect |
| 151. C8 | #13133819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293178 | 2 |
| #20293004 | 2 |
| #20292975 | 2 |
| #20292864 | 2 |
| #20292709 | 2 |
| C4×C8×D107 | 2 |
| #500×C107 | 2 |
| #3169 | 107 |