Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16811066 | C2 | semidirect |
| 2. C2×#16810899 | C2 | semidirect |
| 4. C2×#16810429 | C2 | semidirect |
| 5. C2×#16810426 | C2 | semidirect |
| 6. C2×#16810408 | C2 | semidirect |
| 7. C53×#1387 | C2 | semidirect |
| 47. C2×Dic212 | D4 | semidirect |
| 75. M32×C53 | D4 | semidirect |
| 78. #108×C53 | D4 | semidirect |
| 211. #1387 | D53 | semidirect |
| 242. C53 | #13308 | semidirect |
| 281. M32 | D212 | semidirect |
| 287. #108 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811066 | 2 |
| C2×#16810899 | 2 |
| #20284387 | 2 |
| C2×#16810429 | 2 |
| C2×#16810426 | 2 |
| C2×#16810408 | 2 |
| C53×#1387 | 2 |
| #13308 | 53 |