Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20283311 | C2 | semidirect |
| 3. #20276432 | C2 | semidirect |
| 4. C2×#16810423 | C2 | semidirect |
| 5. C2×#16810408 | C2 | semidirect |
| 6. #20272812 | C2 | semidirect |
| 7. C53×#1387 | C2 | semidirect |
| 14. #16810894 | C4 | semidirect |
| 39. C2×D424 | C2×C4 | semidirect |
| 69. #108×C53 | C2×C4 | semidirect |
| 187. #1387 | D53 | semidirect |
| 216. C53 | #12996 | semidirect |
| 252. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810894 | 2 |
| #20283311 | 2 |
| #20276432 | 2 |
| C2×#16810423 | 2 |
| C2×#16810408 | 2 |
| #20272812 | 2 |
| C53×#1387 | 2 |
| #12996 | 53 |