Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. C2×#16810427 | C2 | semidirect |
| 5. #20272824 | C2 | semidirect |
| 6. #20272810 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 13. #16810895 | C4 | semidirect |
| 51. #13133153 | C2×C4 | semidirect |
| 63. C2×Q16×C53 | C2×C4 | semidirect |
| 178. #2141 | D53 | semidirect |
| 209. C53 | #12997 | semidirect |
| 220. C2×Q16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810895 | 2 |
| #20283312 | 2 |
| C2×#16810427 | 2 |
| C2×#16810408 | 2 |
| #20272824 | 2 |
| #20272810 | 2 |
| C53×#2141 | 2 |
| #12997 | 53 |