Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 3. #20292452 | C2 | semidirect |
| 4. #20292432 | C2 | semidirect |
| 5. #20292430 | C2 | semidirect |
| 7. #367×C107 | C2 | semidirect |
| 66. C107 | #2237 | semidirect |
| 69. #367 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292869 | 2 |
| #20292664 | 2 |
| #20292452 | 2 |
| #20292432 | 2 |
| #20292430 | 2 |
| (C2×D107)⋊C16 | 2 |
| #367×C107 | 2 |
| #2237 | 107 |