Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1022 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 267 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. C22×D848 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. #20276965 | C2 | direct (N × H) |
| 4. C2×C4×C16×C53 | C2 | semidirect |
| 9. C2×D848 | C22 | semidirect |
| 11. #16811000 | C22 | semidirect |
| 14. C4×C16×C53 | C22 | semidirect |
| 28. C2×C16×C53 | D4 | semidirect |
| 51. C16×C53 | C2×D4 | semidirect |
| 56. C2×C4×C53 | D16 | semidirect |
| 77. C4×C53 | C2×D16 | semidirect |
| 83. C2×C4×C16 | D53 | semidirect |
| 84. C2×C53 | #2246 | semidirect |
| 97. C4×C16 | C2×D53 | semidirect |
| 98. C53 | C2×#2246 | semidirect |
| 112. C2×C16 | D212 | semidirect |
| 135. C16 | C2×D212 | semidirect |
| 144. C2×C4 | D848 | semidirect |
| 160. C4 | C2×D848 | semidirect |
| 164. C2 | #20276965 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16811000 | 2 |
| #20276965 | 2 |
| C2×C4×C16×C53 | 2 |
| C2×#2246 | 53 |