Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 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. #20268266 | C2 | semidirect |
| 2. #20267903 | C2 | semidirect |
| 3. D8×Dic103 | C2 | semidirect |
| 4. #20267829 | C2 | semidirect |
| 5. #20267796 | C2 | semidirect |
| 6. #20267746 | C2 | semidirect |
| 10. D4×Dic103 | C22 | semidirect |
| 14. #15692955 | C22 | semidirect |
| 15. #15692953 | C22 | semidirect |
| 16. #15692942 | C22 | semidirect |
| 17. #15692931 | C22 | semidirect |
| 18. C8×Dic103 | C22 | semidirect |
| 20. C2×D8×C103 | C4 | semidirect |
| 37. C2×D4×C103 | C2×C4 | semidirect |
| 40. D8×C103 | C2×C4 | semidirect |
| 41. D8×C103 | C2×C4 | semidirect |
| 42. C2×C8×C103 | C2×C4 | semidirect |
| 78. C103 | #2948 | semidirect |
| 87. C2×D8 | Dic103 | semidirect |
| 105. C2×D4 | C2×Dic103 | semidirect |
| 109. D8 | C2×Dic103 | semidirect |
| 110. D8 | C2×Dic103 | semidirect |
| 113. C2×C8 | C2×Dic103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268266 | 2 |
| #20267903 | 2 |
| D8×Dic103 | 2 |
| #20267829 | 2 |
| #20267796 | 2 |
| #20267746 | 2 |
| C22×D8×C103 | 2 |
| #2948 | 103 |