Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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. C2×#16812128 | C2 | semidirect |
| 2. #20293281 | C2 | semidirect |
| 3. #20293007 | C2 | semidirect |
| 4. #20292869 | C2 | semidirect |
| 5. #20292832 | C2 | semidirect |
| 6. #20292790 | C2 | semidirect |
| 7. C8×D428 | C2 | semidirect |
| 8. C4×D8×C107 | C2 | semidirect |
| 49. D8×C107 | D4 | semidirect |
| 85. C4×C107 | #135 | semidirect |
| 96. C107 | #3283 | semidirect |
| 103. C4×D8 | D107 | semidirect |
| 137. D8 | D428 | semidirect |
| 183. C4 | #16812128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812128 | 2 |
| #20293281 | 2 |
| #20293007 | 2 |
| #20292869 | 2 |
| #20292832 | 2 |
| #20292790 | 2 |
| C8×D428 | 2 |
| C4×D8×C107 | 2 |
| #3283 | 107 |