Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #20293350 | C2 | semidirect |
| 2. #20292989 | C2 | semidirect |
| 3. #20292979 | C2 | semidirect |
| 4. #20292919 | C2 | semidirect |
| 5. #20292904 | C2 | semidirect |
| 7. #20292832 | C2 | semidirect |
| 8. #20292758 | C2 | semidirect |
| 9. #20292727 | C2 | semidirect |
| 11. D4×Q8×C107 | C2 | semidirect |
| 123. C107 | #3367 | semidirect |
| 125. D4×Q8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293350 | 2 |
| #20292989 | 2 |
| #20292979 | 2 |
| #20292919 | 2 |
| #20292904 | 2 |
| #20292842 | 2 |
| #20292832 | 2 |
| #20292758 | 2 |
| #20292727 | 2 |
| C4×#13133803 | 2 |
| D4×Q8×C107 | 2 |
| #3367 | 107 |