Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1762 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1762 conjugacy classes of subgroups — too many to draw. Only its 299 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×#16811011 | C2 | semidirect |
| 2. C2×#16810999 | C2 | semidirect |
| 3. C2×#16810996 | C2 | semidirect |
| 4. C2×#16810995 | C2 | semidirect |
| 5. #20283109 | C2 | semidirect |
| 6. #20283071 | C2 | semidirect |
| 7. C4×#13133127 | C2 | semidirect |
| 8. C2×C53×#493 | C2 | semidirect |
| 52. #13133127 | D4 | semidirect |
| 53. C4×#88322 | D4 | semidirect |
| 66. C4×C8×C53 | D4 | semidirect |
| 139. C8×C53 | #127 | semidirect |
| 140. #88322 | #127 | semidirect |
| 154. C4×C53 | #496 | semidirect |
| 161. C2×#493 | D53 | semidirect |
| 194. C53 | #33304 | semidirect |
| 231. C4×C8 | C22⋊D53 | semidirect |
| 305. C8 | #13133213 | semidirect |
| 320. C4 | #16811011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811011 | 2 |
| C2×#16810999 | 2 |
| C2×#16810996 | 2 |
| C2×#16810995 | 2 |
| #20283109 | 2 |
| #20283071 | 2 |
| C4×#13133127 | 2 |
| C2×C53×#493 | 2 |
| #33304 | 53 |