Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20282602 | C2 | semidirect |
| 4. #20272745 | C2 | semidirect |
| 5. #20272743 | C2 | semidirect |
| 6. #20272648 | C2 | semidirect |
| 89. C2×Dic106 | SD16 | semidirect |
| 207. C53 | #12128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282602 | 2 |
| #20275762 | 2 |
| #20273752 | 2 |
| #20272745 | 2 |
| #20272743 | 2 |
| #20272648 | 2 |
| C53×#1604 | 2 |
| #12128 | 53 |