Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#16812132 | C2 | semidirect |
| 2. #20293060 | C2 | direct (N × H) |
| 3. C2×#16812052 | C2 | semidirect |
| 4. C2×D1712 | C2 | semidirect |
| 5. C2×C16×D107 | C2 | semidirect |
| 6. C2×Q32×C107 | C2 | semidirect |
| 9. #16812132 | C22 | semidirect |
| 13. #16812052 | C22 | semidirect |
| 14. D1712 | C22 | semidirect |
| 16. C16×D107 | C22 | semidirect |
| 18. Q32×C107 | C22 | semidirect |
| 63. C2×C107 | #508 | semidirect |
| 68. C107 | C2×#508 | semidirect |
| 71. C2×Q32 | D107 | semidirect |
| 82. Q32 | C2×D107 | semidirect |
| 133. C2 | #20293060 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| #20293060 | 2 |
| C2×#16812052 | 2 |
| C2×D1712 | 2 |
| C2×C16×D107 | 2 |
| C2×Q32×C107 | 2 |
| C2×#508 | 107 |