Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#15693046 | C2 | semidirect |
| 2. C2×#15693046 | C2 | semidirect |
| 3. #20268558 | C2 | semidirect |
| 4. #20268059 | C2 | semidirect |
| 5. #20268056 | C2 | semidirect |
| 6. #20267839 | C2 | semidirect |
| 7. #20267775 | C2 | semidirect |
| 8. C2×#15692937 | C2 | semidirect |
| 9. #575×C103 | C2 | semidirect |
| 16. C2×#13110092 | C22 | semidirect |
| 18. C2×#13110090 | C22 | semidirect |
| 20. #15693028 | C22 | semidirect |
| 25. #15692956 | C22 | semidirect |
| 26. #15692940 | C22 | semidirect |
| 27. #15692938 | C22 | semidirect |
| 28. #15692937 | C22 | semidirect |
| 32. #137×C103 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C103 | C22 | semidirect |
| 148. C103 | #3068 | semidirect |
| 149. #575 | D103 | semidirect |
| 162. #137 | C2×D103 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693046 | 2 |
| #20268558 | 2 |
| #20268059 | 2 |
| #20268056 | 2 |
| #20267839 | 2 |
| #20267775 | 2 |
| C2×#15692937 | 2 |
| #575×C103 | 2 |
| #3068 | 103 |