Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
250 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 144 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. #20289823 | C2 | semidirect |
| 3. C4×#13133267 | C2 | semidirect |
| 5. #16811556 | C4 | direct (N × H) |
| 14. #13133267 | C2×C4 | semidirect |
| 61. C4×C53 | M64 | semidirect |
| 82. C53 | C4×M64 | semidirect |
| 131. C4 | #16811556 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811556 | 2 |
| #20289823 | 2 |
| C4×#13133267 | 2 |
| C4×C16×D53 | 2 |
| C4×M64 | 53 |