Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×#16811064 | C2 | semidirect |
| 3. C2×#16810432 | C2 | semidirect |
| 4. #20276435 | C2 | semidirect |
| 5. C2×#16810405 | C2 | semidirect |
| 6. #20272822 | C2 | semidirect |
| 7. C2×C53×#470 | C2 | semidirect |
| 50. #13133157 | D4 | semidirect |
| 64. C2×Q16×C53 | D4 | semidirect |
| 79. #106×C53 | D4 | semidirect |
| 208. C2×#470 | D53 | semidirect |
| 242. C53 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D53 | semidirect |
| 289. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20284324 | 2 |
| C2×#16810432 | 2 |
| #20276435 | 2 |
| C2×#16810405 | 2 |
| #20272822 | 2 |
| C2×C53×#470 | 2 |
| #13317 | 53 |