Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20292706 | C2 | semidirect |
| 3. #20292379 | C2 | semidirect |
| 4. D4⋊(C107⋊C8) | C2 | semidirect |
| 5. #20292354 | C2 | semidirect |
| 6. C8×C107⋊C8 | C2 | semidirect |
| 7. #436×C107 | C2 | semidirect |
| 59. C8×C107 | D8 | semidirect |
| 63. C107⋊C8 | M16 | semidirect |
| 84. C107 | #1589 | semidirect |
| 87. #436 | D107 | semidirect |
| 147. C8 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133803 | 2 |
| #20292706 | 2 |
| #20292379 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #20292354 | 2 |
| C8×C107⋊C8 | 2 |
| #436×C107 | 2 |
| #1589 | 107 |