Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 486 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. #20274751 | C2 | semidirect |
| 4. #20272591 | C2 | semidirect |
| 104. C23×C53 | #108 | semidirect |
| 123. C2×C4×C53 | #108 | semidirect |
| 186. C53 | #8611 | semidirect |
| 268. C23 | #13133152 | semidirect |
| 287. C2×C4 | #13133152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#88322 | 2 |
| #20274751 | 2 |
| #20273053 | 2 |
| #20272591 | 2 |
| C53×#1465 | 2 |
| #8611 | 53 |