Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×D428 | C2 | semidirect |
| 2. #20293003 | C2 | semidirect |
| 3. #20292819 | C2 | semidirect |
| 4. #20292370 | C2 | semidirect |
| 5. D4⋊(C107⋊C8) | C2 | semidirect |
| 6. #20292354 | C2 | semidirect |
| 7. #459×C107 | C2 | semidirect |
| 17. C4⋊(C107⋊C8) | C22 | semidirect |
| 19. C4×C107⋊C8 | C22 | semidirect |
| 21. #127×C107 | C22 | semidirect |
| 23. C4⋊C8×C107 | C22 | semidirect |
| 67. D4×C107 | D8 | semidirect |
| 83. D428 | D8 | semidirect |
| 118. C107 | #1619 | semidirect |
| 122. #459 | D107 | semidirect |
| 132. #127 | C2×D107 | semidirect |
| 139. C4⋊C8 | C2×D107 | semidirect |
| 194. D4 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D428 | 2 |
| #20293003 | 2 |
| #20292819 | 2 |
| #20292370 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #20292354 | 2 |
| #459×C107 | 2 |
| #1619 | 107 |