Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
206 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. #20289876 | C2 | direct (N × H) |
| 8. C2×#13133123 | C4 | semidirect |
| 9. C32×D53 | C4 | semidirect |
| 11. C2×C32×C53 | C4 | semidirect |
| 21. #13133123 | C2×C4 | semidirect |
| 23. C32×C53 | C2×C4 | semidirect |
| 65. C2×C53 | #1423 | semidirect |
| 67. D53 | #1423 | semidirect |
| 75. C2×C32 | #6157 | semidirect |
| 78. C53 | C2×#1423 | semidirect |
| 90. C32 | C2×#6157 | semidirect |
| 131. C2 | #20289876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811549 | 2 |
| #20289876 | 2 |
| C2×C32×D53 | 2 |
| C2×#1423 | 53 |