Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20268599 | C2 | semidirect |
| 2. #20268593 | C2 | semidirect |
| 3. #20268176 | C2 | semidirect |
| 4. #20268063 | C2 | semidirect |
| 5. #20268061 | C2 | semidirect |
| 6. #20268056 | C2 | semidirect |
| 7. #20267967 | C2 | semidirect |
| 8. #20267964 | C2 | semidirect |
| 9. #20267908 | C2 | semidirect |
| 10. #20267906 | C2 | semidirect |
| 11. #578×C103 | C2 | semidirect |
| 18. #15693046 | C22 | semidirect |
| 23. C2×#13110092 | C22 | semidirect |
| 26. #15693028 | C22 | semidirect |
| 28. #15693010 | C22 | semidirect |
| 29. #15692957 | C22 | semidirect |
| 30. #15692956 | C22 | semidirect |
| 31. #15692948 | C22 | semidirect |
| 32. #15692948 | C22 | semidirect |
| 34. #15692940 | C22 | semidirect |
| 35. #15692937 | C22 | semidirect |
| 36. C8×Dic103 | C22 | semidirect |
| 37. 2−1+4×C103 | C22 | semidirect |
| 39. #137×C103 | C22 | semidirect |
| 43. C2×Q16×C103 | C22 | semidirect |
| 44. #131×C103 | C22 | semidirect |
| 150. C103 | #3290 | semidirect |
| 151. #578 | D103 | semidirect |
| 162. 2−1+4 | C2×D103 | semidirect |
| 167. #137 | C2×D103 | semidirect |
| 178. C2×Q16 | C2×D103 | semidirect |
| 185. #131 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268599 | 2 |
| #20268593 | 2 |
| #20268176 | 2 |
| #20268063 | 2 |
| #20268061 | 2 |
| #20268056 | 2 |
| #20267967 | 2 |
| #20267964 | 2 |
| #20267908 | 2 |
| #20267906 | 2 |
| #578×C103 | 2 |
| #3290 | 103 |