Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20293262 | C2 | semidirect |
| 2. #20292819 | C2 | semidirect |
| 3. #20292371 | C2 | semidirect |
| 4. #20292356 | C2 | semidirect |
| 5. #493×C107 | C2 | semidirect |
| 11. C4⋊(C107⋊C8) | C22 | semidirect |
| 15. #127×C107 | C22 | semidirect |
| 16. C4×C8×C107 | C22 | semidirect |
| 51. D428 | D8 | semidirect |
| 75. C107 | #1619 | semidirect |
| 77. #493 | D107 | semidirect |
| 85. #127 | C2×D107 | semidirect |
| 91. C4×C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293262 | 2 |
| #20292819 | 2 |
| #20292371 | 2 |
| #20292356 | 2 |
| #493×C107 | 2 |
| #1619 | 107 |