Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20292649 | C2 | semidirect |
| 3. C4×#13133801 | C2 | semidirect |
| 4. Q8⋊(C107⋊C8) | C2 | semidirect |
| 5. #20292356 | C2 | semidirect |
| 6. #20292354 | C2 | semidirect |
| 7. Q8⋊C8×C107 | C2 | semidirect |
| 61. Q8×C107 | M16 | semidirect |
| 73. D428 | M16 | semidirect |
| 111. C107 | #1489 | semidirect |
| 116. Q8⋊C8 | D107 | semidirect |
| 172. Q8 | #13133801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133819 | 2 |
| #20292649 | 2 |
| C4×#13133801 | 2 |
| Q8⋊(C107⋊C8) | 2 |
| #20292356 | 2 |
| #20292354 | 2 |
| Q8⋊C8×C107 | 2 |
| #1489 | 107 |