Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20292680 | C2 | semidirect |
| 3. #20292354 | C2 | semidirect |
| 4. #431×C107 | C2 | semidirect |
| 15. C4×C107⋊C8 | C22 | semidirect |
| 17. C4⋊C8×C107 | C22 | semidirect |
| 23. C2×D428 | C8 | semidirect |
| 88. C107 | #1478 | semidirect |
| 91. #431 | D107 | semidirect |
| 103. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D428 | 2 |
| #20292680 | 2 |
| #20292354 | 2 |
| #431×C107 | 2 |
| #1478 | 107 |