Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 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. C2×#16810445 | C2 | semidirect |
| 4. #20275441 | C2 | semidirect |
| 5. #20272814 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 18. #16810433 | C4 | semidirect |
| 72. Q16×C53 | C4⋊C4 | semidirect |
| 76. D8×C53 | C4⋊C4 | semidirect |
| 180. C53 | #12950 | semidirect |
| 229. Q16 | #11719919 | semidirect |
| 233. D8 | #11719919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810740 | 2 |
| C2×#16810445 | 2 |
| C2×#16810433 | 2 |
| #20275441 | 2 |
| #20272814 | 2 |
| #20272796 | 2 |
| C2×C53×#360 | 2 |
| #12950 | 53 |