Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20293003 | C2 | semidirect |
| 2. #20293003 | C2 | semidirect |
| 3. #20292999 | C2 | semidirect |
| 4. #20292974 | C2 | semidirect |
| 5. #20292973 | C2 | semidirect |
| 6. #20292349 | C2 | semidirect |
| 7. #493×C107 | C2 | semidirect |
| 60. C107⋊C8 | D8 | semidirect |
| 82. C107 | #1721 | semidirect |
| 85. #493 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293003 | 2 |
| #20292999 | 2 |
| #20292974 | 2 |
| #20292973 | 2 |
| #20292349 | 2 |
| #493×C107 | 2 |
| #1721 | 107 |