Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20292757 | C2 | semidirect |
| 4. #20292380 | C2 | semidirect |
| 5. #20292359 | C2 | semidirect |
| 7. #322×C107 | C2 | semidirect |
| 58. C8×C107 | M16 | semidirect |
| 78. C107 | #1592 | semidirect |
| 85. #322 | D107 | semidirect |
| 138. C8 | #13133801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292757 | 2 |
| C4×#13133807 | 2 |
| #20292706 | 2 |
| #20292380 | 2 |
| #20292359 | 2 |
| #20292356 | 2 |
| #322×C107 | 2 |
| #1592 | 107 |