Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13110106 | C2 | semidirect |
| 2. C22×#13110092 | C2 | semidirect |
| 3. C22×D824 | C2 | semidirect |
| 4. C2×#15692996 | C2 | semidirect |
| 5. #20267939 | C2 | direct (N × H) |
| 6. C2×#15692941 | C2 | semidirect |
| 7. C2×(C2×D103)⋊C8 | C2 | semidirect |
| 8. C2×#103×C103 | C2 | semidirect |
| 12. C2×#13110106 | C22 | semidirect |
| 20. C2×#13110092 | C22 | semidirect |
| 22. C2×D824 | C22 | semidirect |
| 25. #15692996 | C22 | semidirect |
| 27. #15692941 | C22 | semidirect |
| 28. (C2×D103)⋊C8 | C22 | semidirect |
| 32. #103×C103 | C22 | semidirect |
| 48. C2×D412 | D4 | semidirect |
| 65. C2×Q8×C103 | D4 | semidirect |
| 89. Q8×C103 | C2×D4 | semidirect |
| 107. D412 | C2×D4 | semidirect |
| 136. C2×C103 | #449 | semidirect |
| 144. C103 | C2×#449 | semidirect |
| 150. C2×#103 | D103 | semidirect |
| 174. #103 | C2×D103 | semidirect |
| 185. C2×Q8 | D412 | semidirect |
| 233. Q8 | C2×D412 | semidirect |
| 283. C2 | #20267939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13110106 | 2 |
| C22×#13110092 | 2 |
| C22×D824 | 2 |
| C2×#15692996 | 2 |
| #20267939 | 2 |
| C2×#15692941 | 2 |
| C2×(C2×D103)⋊C8 | 2 |
| C2×#103×C103 | 2 |
| C2×#449 | 103 |