Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1270 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1270 conjugacy classes of subgroups — too many to draw. Only its 251 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. C2×#16810859 | C2 | semidirect |
| 2. #20283060 | C2 | semidirect |
| 3. #20276242 | C2 | semidirect |
| 4. #20275788 | C2 | semidirect |
| 5. C2×C53×#336 | C2 | semidirect |
| 38. C22×C8×C53 | D4 | semidirect |
| 50. C22×C4×C53 | D8 | semidirect |
| 132. C2×#336 | D53 | semidirect |
| 153. C53 | #30239 | semidirect |
| 164. C22×C8 | D212 | semidirect |
| 195. C22×C4 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| #20283060 | 2 |
| #20276242 | 2 |
| #20275788 | 2 |
| C2×C53×#336 | 2 |
| #30239 | 53 |