Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
716 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 716 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. #20275030 | C2 | semidirect |
| 3. C2×#16810358 | C2 | semidirect |
| 4. #20272971 | C2 | semidirect |
| 5. C53×#1280 | C2 | semidirect |
| 46. #13133124 | D4 | semidirect |
| 219. #1280 | D53 | semidirect |
| 246. C53 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280817 | 2 |
| #20275030 | 2 |
| C2×#16810358 | 2 |
| #20272971 | 2 |
| C53×#1280 | 2 |
| #10403 | 53 |