Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
918 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 918 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×#13133162 | C2 | semidirect |
| 2. C2×#16811003 | C2 | semidirect |
| 4. #20276971 | C2 | direct (N × H) |
| 5. C2×C4×C16×C53 | C2 | semidirect |
| 13. C2×#13133162 | C22 | semidirect |
| 15. #16811003 | C22 | semidirect |
| 20. C4×C16×C53 | C22 | semidirect |
| 43. C2×C16×C53 | D4 | semidirect |
| 75. C16×C53 | C2×D4 | semidirect |
| 80. C2×C4×C53 | SD32 | semidirect |
| 106. C4×C53 | C2×SD32 | semidirect |
| 114. C2×C4×C16 | D53 | semidirect |
| 115. C2×C53 | #2248 | semidirect |
| 133. C4×C16 | C2×D53 | semidirect |
| 134. C53 | C2×#2248 | semidirect |
| 157. C2×C16 | D212 | semidirect |
| 189. C16 | C2×D212 | semidirect |
| 203. C2×C4 | #13133162 | semidirect |
| 220. C4 | C2×#13133162 | semidirect |
| 224. C2 | #20276971 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| C2×#16811003 | 2 |
| C2×#16811000 | 2 |
| #20276971 | 2 |
| C2×C4×C16×C53 | 2 |
| C2×#2248 | 53 |