Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D103 | C2 | semidirect |
| 2. C2×#15693053 | C2 | semidirect |
| 4. #20267946 | C2 | semidirect |
| 5. #20267945 | C2 | semidirect |
| 6. #20267932 | C2 | semidirect |
| 7. #20267931 | C2 | semidirect |
| 8. #20267930 | C2 | semidirect |
| 9. #20267798 | C2 | semidirect |
| 10. #20267753 | C2 | semidirect |
| 11. #451×C103 | C2 | semidirect |
| 23. C2×#13110095 | C22 | semidirect |
| 24. C2×#13110094 | C22 | semidirect |
| 25. C2×#13110092 | C22 | semidirect |
| 35. #15692946 | C22 | semidirect |
| 36. #15692945 | C22 | semidirect |
| 37. #15692944 | C22 | semidirect |
| 41. C2×Q16×C103 | C22 | semidirect |
| 43. #103×C103 | C22 | semidirect |
| 58. Q8×D103 | D4 | semidirect |
| 141. C22×C103 | #137 | semidirect |
| 152. C2×D103 | #137 | semidirect |
| 170. C103 | #3004 | semidirect |
| 176. #451 | D103 | semidirect |
| 195. C2×Q16 | C2×D103 | semidirect |
| 211. #103 | C2×D103 | semidirect |
| 321. C22 | #15693053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D103 | 2 |
| C2×#15693053 | 2 |
| #20268304 | 2 |
| #20267946 | 2 |
| #20267945 | 2 |
| #20267932 | 2 |
| #20267931 | 2 |
| #20267930 | 2 |
| #20267798 | 2 |
| #20267753 | 2 |
| #451×C103 | 2 |
| #3004 | 103 |