Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20283515 | C2 | semidirect |
| 3. C2×#16810434 | C2 | semidirect |
| 4. #20275592 | C2 | semidirect |
| 5. #20272820 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C53×#2140 | C2 | semidirect |
| 11. #16811059 | C4 | semidirect |
| 48. #13133157 | C2×C4 | semidirect |
| 63. C2×D8×C53 | C2×C4 | semidirect |
| 115. Dic212 | C22⋊C4 | semidirect |
| 117. D424 | C22⋊C4 | semidirect |
| 182. #2140 | D53 | semidirect |
| 212. C53 | #13025 | semidirect |
| 227. 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 |
| #20283515 | 2 |
| C2×#16810434 | 2 |
| #20275592 | 2 |
| #20272820 | 2 |
| #20272798 | 2 |
| C53×#2140 | 2 |
| #13025 | 53 |