Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#16810446 | C2 | semidirect |
| 4. #20275496 | C2 | semidirect |
| 5. #20272826 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 23. C53×#362 | C4 | semidirect |
| 24. C53×#361 | C4 | semidirect |
| 165. #362 | Dic53 | semidirect |
| 166. #361 | Dic53 | semidirect |
| 169. C53 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283632 | 2 |
| C2×#16810446 | 2 |
| C2×#16810433 | 2 |
| #20275496 | 2 |
| #20272826 | 2 |
| #20272802 | 2 |
| C53×#2148 | 2 |
| #12952 | 53 |