Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283592 | C2 | semidirect |
| 3. C2×#16810429 | C2 | semidirect |
| 4. C2×#16810424 | C2 | semidirect |
| 5. #20272825 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#1978 | C2 | semidirect |
| 11. #16811059 | C4 | semidirect |
| 45. #13133157 | C2×C4 | semidirect |
| 60. C2×D8×C53 | C2×C4 | semidirect |
| 186. #1978 | D53 | semidirect |
| 216. C53 | #13022 | semidirect |
| 231. C2×D8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811059 | 2 |
| #20283592 | 2 |
| C2×#16810429 | 2 |
| C2×#16810424 | 2 |
| #20272825 | 2 |
| #20272804 | 2 |
| C53×#1978 | 2 |
| #13022 | 53 |