Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20293297 | C2 | semidirect |
| 3. #20292860 | C2 | semidirect |
| 4. #20292824 | C2 | semidirect |
| 5. #20292769 | C2 | semidirect |
| 6. C4×Dic428 | C2 | semidirect |
| 7. C8×D428 | C2 | semidirect |
| 8. #493×C107 | C2 | semidirect |
| 37. Dic428 | D4 | semidirect |
| 86. C4×C107 | #135 | semidirect |
| 98. C107 | #3287 | semidirect |
| 101. #493 | D107 | semidirect |
| 187. 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 |
| #20293297 | 2 |
| #20292860 | 2 |
| #20292824 | 2 |
| #20292769 | 2 |
| C4×Dic428 | 2 |
| C8×D428 | 2 |
| #493×C107 | 2 |
| #3287 | 107 |