Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #20283307 | C2 | semidirect |
| 3. #20276450 | C2 | semidirect |
| 4. C2×#16810434 | C2 | semidirect |
| 5. #20276342 | C2 | semidirect |
| 6. #20272815 | C2 | semidirect |
| 7. C53×#1389 | C2 | semidirect |
| 13. #16810899 | C4 | semidirect |
| 14. #16810894 | C4 | semidirect |
| 40. C2×Dic212 | C2×C4 | semidirect |
| 42. C2×D424 | C2×C4 | semidirect |
| 72. #108×C53 | C2×C4 | semidirect |
| 193. #1389 | D53 | semidirect |
| 222. C53 | #13005 | semidirect |
| 260. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284436 | 2 |
| #20283307 | 2 |
| #20276450 | 2 |
| C2×#16810434 | 2 |
| #20276342 | 2 |
| #20272815 | 2 |
| C53×#1389 | 2 |
| #13005 | 53 |