Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
918 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 251 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×#13133161 | C2 | semidirect |
| 2. C2×#16811003 | C2 | semidirect |
| 3. #20276970 | C2 | direct (N × H) |
| 4. C2×C4×#11719908 | C2 | semidirect |
| 10. C2×#13133161 | C22 | semidirect |
| 13. #16811003 | C22 | semidirect |
| 14. C4×#11719908 | C22 | semidirect |
| 31. C2×#11719908 | D4 | semidirect |
| 75. #11719908 | C2×D4 | semidirect |
| 84. C2×C4×C53 | SD32 | semidirect |
| 106. C4×C53 | C2×SD32 | semidirect |
| 116. C2×C53 | #2248 | semidirect |
| 134. C53 | C2×#2248 | semidirect |
| 203. C2×C4 | #13133161 | semidirect |
| 220. C4 | C2×#13133161 | semidirect |
| 224. C2 | #20276970 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133161 | 2 |
| C2×#16811003 | 2 |
| #20276970 | 2 |
| C2×C4×#11719908 | 2 |
| C2×C53×#493 | 2 |
| C2×#2248 | 53 |