Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
278 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20292827 | C2 | semidirect |
| 3. #20292822 | C2 | semidirect |
| 4. #20292371 | C2 | semidirect |
| 5. Q8⋊(C107⋊C8) | C2 | semidirect |
| 6. D4⋊(C107⋊C8) | C2 | semidirect |
| 7. #550×C107 | C2 | semidirect |
| 56. Q8×C107 | D8 | semidirect |
| 108. C107 | #1621 | semidirect |
| 109. #550 | D107 | semidirect |
| 164. Q8 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293003 | 2 |
| #20292827 | 2 |
| #20292822 | 2 |
| #20292371 | 2 |
| Q8⋊(C107⋊C8) | 2 |
| D4⋊(C107⋊C8) | 2 |
| #550×C107 | 2 |
| #1621 | 107 |