Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 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. #20276503 | C2 | semidirect |
| 3. C2×#16810448 | C2 | semidirect |
| 6. #20272812 | C2 | semidirect |
| 7. C53×#1387 | C2 | semidirect |
| 21. #16810408 | C4 | semidirect |
| 43. C2×#11719908 | C2×C4 | semidirect |
| 57. M32×C53 | C2×C4 | semidirect |
| 157. #1387 | D53 | semidirect |
| 183. C53 | #12925 | semidirect |
| 203. M32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283311 | 2 |
| #20276503 | 2 |
| C2×#16810448 | 2 |
| C2×#16810408 | 2 |
| #20274776 | 2 |
| #20272812 | 2 |
| C53×#1387 | 2 |
| #12925 | 53 |