Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
994 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 224 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×#16811489 | C2 | semidirect |
| 2. #20289531 | C2 | direct (N × H) |
| 6. #16811489 | C22 | semidirect |
| 36. C22×D4×C53 | C8 | semidirect |
| 54. C2×D4×C53 | C2×C8 | semidirect |
| 151. C2×C53 | #1270 | semidirect |
| 167. C53 | C2×#1270 | semidirect |
| 173. C22×D4 | #88324 | semidirect |
| 208. C2×D4 | C2×#88324 | semidirect |
| 301. C2 | #20289531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811489 | 2 |
| #20289531 | 2 |
| C2×#16810526 | 2 |
| C2×#1270 | 53 |