Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276970 | C2 | semidirect |
| 2. #20276760 | C2 | semidirect |
| 3. #20274080 | C2 | semidirect |
| 4. #20272761 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 10. #16811003 | C22 | semidirect |
| 12. C4⋊#11719908 | C22 | semidirect |
| 14. C4×#11719908 | C22 | semidirect |
| 15. #16810376 | C22 | semidirect |
| 112. D4×C53 | SD32 | semidirect |
| 180. C53 | #12320 | semidirect |
| 270. D4 | #13133161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276970 | 2 |
| #20276760 | 2 |
| #20274080 | 2 |
| #20272761 | 2 |
| #20272676 | 2 |
| D4⋊#11719908 | 2 |
| D4×D8×C53 | 2 |
| #12320 | 53 |