Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×D824 | C2 | semidirect |
| 2. #20268226 | C2 | direct (N × H) |
| 3. C2×#15692964 | C2 | semidirect |
| 4. C2×#15692962 | C2 | semidirect |
| 5. C2×#15692961 | C2 | semidirect |
| 6. C2×#135×C103 | C2 | semidirect |
| 11. C2×D824 | C22 | semidirect |
| 12. #15692964 | C22 | semidirect |
| 13. #15692962 | C22 | semidirect |
| 14. #15692961 | C22 | semidirect |
| 15. C2×C103⋊C16 | C22 | semidirect |
| 18. #135×C103 | C22 | semidirect |
| 19. C2×Q16×C103 | C22 | semidirect |
| 21. C2×D8×C103 | C22 | semidirect |
| 31. C103⋊C16 | C23 | semidirect |
| 40. Q16×C103 | C23 | semidirect |
| 43. D8×C103 | C23 | semidirect |
| 84. C2×C103 | #509 | semidirect |
| 88. C103 | C2×#509 | semidirect |
| 89. C2×#135 | D103 | semidirect |
| 98. #135 | C2×D103 | semidirect |
| 99. C2×Q16 | C2×D103 | semidirect |
| 105. C2×D8 | C2×D103 | semidirect |
| 124. Q16 | C22×D103 | semidirect |
| 130. D8 | C22×D103 | semidirect |
| 173. C2 | #20268226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D824 | 2 |
| #20268226 | 2 |
| C2×#15692964 | 2 |
| C2×#15692962 | 2 |
| C2×#15692961 | 2 |
| C2×#135×C103 | 2 |
| C2×#509 | 103 |