Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20291078 | C2 | semidirect |
| 2. C4×#13133288 | C2 | semidirect |
| 3. #20289706 | C2 | semidirect |
| 4. #20289705 | C2 | semidirect |
| 171. C53 | #11751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291078 | 2 |
| C4×#13133288 | 2 |
| #20289706 | 2 |
| #20289705 | 2 |
| #20285291 | 2 |
| #11751 | 53 |