Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20293003 | C2 | semidirect |
| 2. #20292822 | C2 | semidirect |
| 3. #20292371 | C2 | semidirect |
| 4. D4⋊(C107⋊C8) | C2 | semidirect |
| 5. D42×C107 | C2 | semidirect |
| 8. #16812106 | C22 | semidirect |
| 9. C4⋊(C107⋊C8) | C22 | semidirect |
| 11. C4×C107⋊C8 | C22 | semidirect |
| 45. D4×C107 | D8 | semidirect |
| 75. C107 | #1619 | semidirect |
| 76. D42 | D107 | semidirect |
| 123. D4 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293003 | 2 |
| #20292822 | 2 |
| #20292371 | 2 |
| D4⋊(C107⋊C8) | 2 |
| D42×C107 | 2 |
| #1619 | 107 |