Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20289873 | C2 | semidirect |
| 3. C4⋊#13133267 | C2 | semidirect |
| 70. C4×C53 | M64 | semidirect |
| 75. Dic53 | M64 | semidirect |
| 93. C53 | #13627 | semidirect |
| 152. C4 | #16811556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811556 | 2 |
| #20289873 | 2 |
| C4⋊#13133267 | 2 |
| C4×C16×D53 | 2 |
| #13627 | 53 |