Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20291131 | C2 | semidirect |
| 3. #20289738 | C2 | semidirect |
| 4. #20289682 | C2 | semidirect |
| 6. #20289627 | C2 | semidirect |
| 67. #11719910 | SD16 | semidirect |
| 128. C53 | #12049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291131 | 2 |
| D4×#11719910 | 2 |
| #20289738 | 2 |
| #20289682 | 2 |
| D4⋊#11719910 | 2 |
| #20289627 | 2 |
| #20273518 | 2 |
| #12049 | 53 |