Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 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. #41×Dic103 | C2 | semidirect |
| 2. #20267903 | C2 | semidirect |
| 3. #20267898 | C2 | semidirect |
| 4. #20267892 | C2 | semidirect |
| 5. #20267829 | C2 | semidirect |
| 6. #20267787 | C2 | semidirect |
| 7. C2×#15692931 | C2 | semidirect |
| 24. #135×C103 | C4 | semidirect |
| 42. #41×C103 | C2×C4 | semidirect |
| 48. Q16×C103 | C2×C4 | semidirect |
| 49. SD16×C103 | C2×C4 | semidirect |
| 50. D8×C103 | C2×C4 | semidirect |
| 51. C2×C8×C103 | C2×C4 | semidirect |
| 90. C103 | #2943 | semidirect |
| 100. #135 | Dic103 | semidirect |
| 120. #41 | C2×Dic103 | semidirect |
| 128. Q16 | C2×Dic103 | semidirect |
| 129. SD16 | C2×Dic103 | semidirect |
| 130. D8 | C2×Dic103 | semidirect |
| 133. C2×C8 | C2×Dic103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic103 | 2 |
| #20267903 | 2 |
| #20267898 | 2 |
| #20267892 | 2 |
| #20267829 | 2 |
| #20267787 | 2 |
| C2×#15692931 | 2 |
| C2×#135×C103 | 2 |
| #2943 | 103 |