Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1124 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 254 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×#16811658 | C2 | semidirect |
| 2. #20290836 | C2 | semidirect |
| 3. #20290692 | C2 | semidirect |
| 4. C4×C4⋊#88324 | C2 | semidirect |
| 26. C4⋊#88324 | D4 | semidirect |
| 71. C42×C53 | M16 | semidirect |
| 124. C4×C53 | #436 | semidirect |
| 157. C53 | #23176 | semidirect |
| 218. C42 | #11719940 | semidirect |
| 266. C4 | #16811658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811658 | 2 |
| #20290836 | 2 |
| #20290692 | 2 |
| C4×C4⋊#88324 | 2 |
| #127×Dic53 | 2 |
| #23176 | 53 |