Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293444 | C2 | semidirect |
| 2. #20293068 | C2 | semidirect |
| 3. #20293067 | C2 | semidirect |
| 4. #20293057 | C2 | semidirect |
| 5. C2×#16812055 | C2 | semidirect |
| 6. #20293044 | C2 | semidirect |
| 7. #578×C107 | C2 | semidirect |
| 74. C107 | #3417 | semidirect |
| 76. #578 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293444 | 2 |
| #20293068 | 2 |
| #20293067 | 2 |
| #20293057 | 2 |
| C2×#16812055 | 2 |
| #20293044 | 2 |
| #578×C107 | 2 |
| #3417 | 107 |