Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20293068 | C2 | direct (N × H) |
| 3. C2×#16812055 | C2 | semidirect |
| 4. C2×#16812052 | C2 | semidirect |
| 5. C2×#16812049 | C2 | semidirect |
| 6. C22×Q16×C107 | C2 | semidirect |
| 13. #16812055 | C22 | semidirect |
| 14. #16812052 | C22 | semidirect |
| 15. #16812049 | C22 | semidirect |
| 21. C2×Q16×C107 | C22 | semidirect |
| 80. C2×C107 | #510 | semidirect |
| 84. C107 | C2×#510 | semidirect |
| 86. C22×Q16 | D107 | semidirect |
| 99. C2×Q16 | C2×D107 | semidirect |
| 165. C2 | #20293068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293068 | 2 |
| C2×#16812055 | 2 |
| C2×#16812052 | 2 |
| C2×#16812049 | 2 |
| C22×Q16×C107 | 2 |
| C2×#510 | 107 |