Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20293110 | C2 | semidirect |
| 3. #20292633 | C2 | semidirect |
| 4. #20292529 | C2 | semidirect |
| 5. #20292395 | C2 | semidirect |
| 6. #20292387 | C2 | semidirect |
| 7. C2×#104×C107 | C2 | semidirect |
| 10. #16812134 | C4 | semidirect |
| 34. C2×D428 | C2×C4 | semidirect |
| 40. #13133802 | C2×C4 | semidirect |
| 75. Q8×C107 | C22⋊C4 | semidirect |
| 79. D4×C107 | C22⋊C4 | semidirect |
| 133. C107 | #1883 | semidirect |
| 136. C2×#104 | D107 | semidirect |
| 208. Q8 | (C2×D107)⋊C4 | semidirect |
| 216. D4 | (C2×D107)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| #20293110 | 2 |
| #20292633 | 2 |
| #20292529 | 2 |
| #20292395 | 2 |
| #20292387 | 2 |
| C2×#104×C107 | 2 |
| #1883 | 107 |