Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20283516 | C2 | semidirect |
| 3. #20276432 | C2 | semidirect |
| 4. #20275589 | C2 | semidirect |
| 5. #20272822 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C2×C53×#360 | C2 | semidirect |
| 11. #16811058 | C4 | semidirect |
| 34. C2×D424 | C2×C4 | semidirect |
| 47. #13133157 | C2×C4 | semidirect |
| 91. Q16×C53 | C22⋊C4 | semidirect |
| 95. D8×C53 | C22⋊C4 | semidirect |
| 181. C2×#360 | D53 | semidirect |
| 212. C53 | #13025 | semidirect |
| 276. Q16 | #11719921 | semidirect |
| 284. D8 | #11719921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| #20283516 | 2 |
| #20276432 | 2 |
| #20275589 | 2 |
| #20272822 | 2 |
| #20272798 | 2 |
| C2×C53×#360 | 2 |
| #13025 | 53 |