Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 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. #20293362 | C2 | semidirect |
| 2. #20293011 | C2 | semidirect |
| 4. #20292843 | C2 | semidirect |
| 5. #20292828 | C2 | semidirect |
| 6. C4×Dic428 | C2 | semidirect |
| 7. C4×D856 | C2 | semidirect |
| 8. C8×Q8×C107 | C2 | semidirect |
| 87. C107 | #3396 | semidirect |
| 93. C8×Q8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293362 | 2 |
| #20293011 | 2 |
| #20293004 | 2 |
| #20292843 | 2 |
| #20292828 | 2 |
| C4×Dic428 | 2 |
| C4×D856 | 2 |
| C8×Q8×C107 | 2 |
| #3396 | 107 |