Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20291577 | C2 | semidirect |
| 2. #20290014 | C2 | semidirect |
| 3. #20290014 | C2 | semidirect |
| 4. #20289955 | C2 | semidirect |
| 5. #20289555 | C2 | semidirect |
| 6. #20289541 | C2 | semidirect |
| 81. C2×D4×C53 | M16 | semidirect |
| 101. C2×C8×C53 | M16 | semidirect |
| 221. C53 | #9093 | semidirect |
| 275. C2×D4 | #11719940 | semidirect |
| 299. C2×C8 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291577 | 2 |
| #20290014 | 2 |
| #20289955 | 2 |
| #20289555 | 2 |
| #20289541 | 2 |
| C2×#16810735 | 2 |
| #9093 | 53 |