Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1132 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 163 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. #20289120 | C2 | semidirect |
| 2. #20285633 | C2 | semidirect |
| 3. #20273796 | C2 | semidirect |
| 4. #20273767 | C2 | semidirect |
| 5. #20273377 | C2 | semidirect |
| 6. #20273133 | C2 | semidirect |
| 7. C53×#3151 | C2 | semidirect |
| 9. #16811339 | C22 | semidirect |
| 12. #16811258 | C22 | semidirect |
| 18. #16810815 | C22 | semidirect |
| 20. #16810676 | C22 | semidirect |
| 21. #16810372 | C22 | semidirect |
| 22. #16810367 | C22 | semidirect |
| 23. #16810352 | C22 | semidirect |
| 26. C2×#127×C53 | C22 | semidirect |
| 29. C53×#492 | C22 | semidirect |
| 30. C4×M16×C53 | C22 | semidirect |
| 176. #3151 | D53 | semidirect |
| 197. C2×#127 | C2×D53 | semidirect |
| 201. #492 | C2×D53 | semidirect |
| 206. C4×M16 | C2×D53 | semidirect |
| 210. C53 | #18714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20285633 | 2 |
| #20273796 | 2 |
| #20273767 | 2 |
| #20273377 | 2 |
| #20273133 | 2 |
| C53×#3151 | 2 |
| #18714 | 53 |