Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20268591 | C2 | semidirect |
| 2. C2×#15693047 | C2 | semidirect |
| 3. C2×#15693047 | C2 | semidirect |
| 4. #20268557 | C2 | semidirect |
| 5. #20268060 | C2 | semidirect |
| 6. #20268053 | C2 | semidirect |
| 7. #20267839 | C2 | semidirect |
| 8. #20267773 | C2 | semidirect |
| 9. C2×#100×C103 | C2 | semidirect |
| 13. #15693054 | C22 | semidirect |
| 15. #15693049 | C22 | semidirect |
| 22. C2×#13110093 | C22 | semidirect |
| 24. C2×#13110090 | C22 | semidirect |
| 25. #15693029 | C22 | semidirect |
| 30. #15692956 | C22 | semidirect |
| 31. #15692939 | C22 | semidirect |
| 32. #15692937 | C22 | semidirect |
| 36. #100×C103 | C22 | semidirect |
| 148. C103 | #3068 | semidirect |
| 157. C2×#100 | D103 | semidirect |
| 184. #100 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268591 | 2 |
| C2×#15693047 | 2 |
| #20268557 | 2 |
| #20268060 | 2 |
| #20268053 | 2 |
| #20267839 | 2 |
| #20267773 | 2 |
| C2×#100×C103 | 2 |
| #3068 | 103 |