Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C22×Dic428 | C2 | semidirect |
| 2. C2×Q16×D107 | C2 | semidirect |
| 4. #20293005 | C2 | semidirect |
| 5. #20292869 | C2 | semidirect |
| 6. #20292836 | C2 | semidirect |
| 7. #20292784 | C2 | semidirect |
| 8. #20292782 | C2 | semidirect |
| 9. #20292721 | C2 | semidirect |
| 11. #467×C107 | C2 | semidirect |
| 55. Dic428 | D4 | semidirect |
| 90. C22⋊D107 | Q16 | semidirect |
| 112. C22×C107 | C2×Q16 | semidirect |
| 116. C2×D107 | C2×Q16 | semidirect |
| 126. Dic107 | C2×Q16 | semidirect |
| 133. C107 | D4×Q16 | semidirect |
| 139. #467 | D107 | semidirect |
| 248. C22 | Q16×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic428 | 2 |
| C2×Q16×D107 | 2 |
| #20293290 | 2 |
| #20293005 | 2 |
| #20292869 | 2 |
| #20292836 | 2 |
| #20292784 | 2 |
| #20292782 | 2 |
| #20292721 | 2 |
| C8×C22⋊D107 | 2 |
| #467×C107 | 2 |
| D4×Q16 | 107 |