Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #20293343 | C2 | direct (N × H) |
| 2. C2×#16812098 | C2 | semidirect |
| 3. C2×#16812084 | C2 | semidirect |
| 4. C2×C4×D428 | C2 | semidirect |
| 5. C2×#16812067 | C2 | semidirect |
| 6. C2×C4⋊Q8×C107 | C2 | semidirect |
| 10. #16812098 | C22 | semidirect |
| 11. #16812084 | C22 | semidirect |
| 12. C4×D428 | C22 | semidirect |
| 13. #16812067 | C22 | semidirect |
| 19. C4⋊Q8×C107 | C22 | semidirect |
| 69. C2×C107 | #555 | semidirect |
| 74. C107 | C2×#555 | semidirect |
| 76. C2×C4⋊Q8 | D107 | semidirect |
| 85. C4⋊Q8 | C2×D107 | semidirect |
| 144. C2 | #20293343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293343 | 2 |
| C2×#16812098 | 2 |
| C2×#16812084 | 2 |
| C2×C4×D428 | 2 |
| C2×#16812067 | 2 |
| C2×C4⋊Q8×C107 | 2 |
| C2×#555 | 107 |