Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1152 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 155 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×#16811365 | C2 | semidirect |
| 2. #20285698 | C2 | semidirect |
| 3. #20274019 | C2 | semidirect |
| 4. #20274003 | C2 | semidirect |
| 5. #20273339 | C2 | semidirect |
| 6. #20273312 | C2 | semidirect |
| 7. C53×#3153 | C2 | semidirect |
| 16. #16811010 | C22 | semidirect |
| 17. #16810985 | C22 | semidirect |
| 21. #16810680 | C22 | semidirect |
| 22. #16810363 | C22 | semidirect |
| 23. #16810362 | C22 | semidirect |
| 26. C53×#532 | C22 | semidirect |
| 28. C53×#497 | C22 | semidirect |
| 29. C53×#496 | C22 | semidirect |
| 31. C4×M16×C53 | C22 | semidirect |
| 60. #13133128 | C23 | semidirect |
| 71. C4⋊Q8×C53 | C23 | semidirect |
| 72. #127×C53 | C23 | semidirect |
| 81. #97×C53 | C23 | semidirect |
| 203. #3153 | D53 | semidirect |
| 219. #532 | C2×D53 | semidirect |
| 226. #497 | C2×D53 | semidirect |
| 228. #496 | C2×D53 | semidirect |
| 235. C4×M16 | C2×D53 | semidirect |
| 238. C53 | #18992 | semidirect |
| 256. C4⋊Q8 | C22×D53 | semidirect |
| 257. #127 | C22×D53 | semidirect |
| 288. #97 | C22×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811365 | 2 |
| #20285698 | 2 |
| #20274019 | 2 |
| #20274003 | 2 |
| #20273339 | 2 |
| #20273312 | 2 |
| C53×#3153 | 2 |
| #18992 | 53 |