Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20292650 | C2 | semidirect |
| 5. #20292399 | C2 | semidirect |
| 6. #20292388 | C2 | semidirect |
| 7. #430×C107 | C2 | semidirect |
| 17. #16812035 | C4 | semidirect |
| 18. #16812035 | C4 | semidirect |
| 98. C107 | #1861 | semidirect |
| 100. #430 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293393 | 2 |
| #20292650 | 2 |
| #20292643 | 2 |
| C2×#16812035 | 2 |
| #20292399 | 2 |
| #20292388 | 2 |
| #430×C107 | 2 |
| #1861 | 107 |