Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#16812130 | C2 | semidirect |
| 3. C2×#16812128 | C2 | semidirect |
| 4. #20293176 | C2 | semidirect |
| 5. #20293011 | C2 | semidirect |
| 6. #20293009 | C2 | semidirect |
| 7. #20293005 | C2 | semidirect |
| 8. #20293002 | C2 | semidirect |
| 9. #20292998 | C2 | semidirect |
| 10. C4×C8×D107 | C2 | semidirect |
| 11. #495×C107 | C2 | semidirect |
| 62. C8×D107 | D4 | semidirect |
| 63. C8×D107 | D4 | semidirect |
| 119. Dic107 | #135 | semidirect |
| 126. C107 | #3147 | semidirect |
| 133. #495 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| C2×#16812130 | 2 |
| C2×#16812128 | 2 |
| #20293176 | 2 |
| #20293011 | 2 |
| #20293009 | 2 |
| #20293005 | 2 |
| #20293002 | 2 |
| #20292998 | 2 |
| C4×C8×D107 | 2 |
| #495×C107 | 2 |
| #3147 | 107 |