Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 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. #20276938 | C2 | semidirect |
| 2. #20276862 | C2 | semidirect |
| 3. #20274114 | C2 | semidirect |
| 4. #20272761 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 8. #16811028 | C22 | semidirect |
| 11. C4⋊#11719908 | C22 | semidirect |
| 14. C4×#11719908 | C22 | semidirect |
| 15. #16810376 | C22 | semidirect |
| 174. C53 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276938 | 2 |
| #20276862 | 2 |
| #20274114 | 2 |
| #20272761 | 2 |
| #20272676 | 2 |
| D4⋊#11719908 | 2 |
| D4×D8×C53 | 2 |
| #12372 | 53 |