Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. #20268444 | C2 | semidirect |
| 2. D4×D412 | C2 | semidirect |
| 3. #20268139 | C2 | semidirect |
| 4. #20268106 | C2 | semidirect |
| 5. #20268028 | C2 | semidirect |
| 6. #20267987 | C2 | semidirect |
| 7. #20267926 | C2 | semidirect |
| 8. C4×#13110090 | C2 | semidirect |
| 9. #20267856 | C2 | semidirect |
| 10. #102×D103 | C2 | semidirect |
| 11. #474×C103 | C2 | semidirect |
| 15. C2×D824 | C22 | semidirect |
| 17. C2×C8×D103 | C22 | semidirect |
| 22. #15692996 | C22 | semidirect |
| 26. C4×D412 | C22 | semidirect |
| 27. C4⋊C4×D103 | C22 | semidirect |
| 28. #15692954 | C22 | semidirect |
| 29. #15692943 | C22 | semidirect |
| 31. #15692941 | C22 | semidirect |
| 32. #15692941 | C22 | semidirect |
| 33. #15692941 | C22 | semidirect |
| 34. (C2×D103)⋊C8 | C22 | semidirect |
| 35. C4×C103⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C103 | C22 | semidirect |
| 38. #107×C103 | C22 | semidirect |
| 39. C4⋊C8×C103 | C22 | semidirect |
| 87. D4×C103 | #41 | semidirect |
| 105. D412 | D8 | semidirect |
| 143. C103 | #3294 | semidirect |
| 148. #474 | D103 | semidirect |
| 161. C4⋊Q8 | C2×D103 | semidirect |
| 174. #107 | C2×D103 | semidirect |
| 175. C4⋊C8 | C2×D103 | semidirect |
| 240. D4 | #13110106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268444 | 2 |
| D4×D412 | 2 |
| #20268139 | 2 |
| #20268106 | 2 |
| #20268028 | 2 |
| #20267987 | 2 |
| #20267926 | 2 |
| C4×#13110090 | 2 |
| #20267856 | 2 |
| #102×D103 | 2 |
| #474×C103 | 2 |
| #3294 | 103 |