Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. #20289748 | C2 | semidirect |
| 4. #20289746 | C2 | semidirect |
| 34. M32×C53 | C8 | semidirect |
| 54. C16×C53 | C2×C8 | semidirect |
| 110. C53 | #12009 | semidirect |
| 116. M32 | #88324 | semidirect |
| 148. C16 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290262 | 2 |
| C2×#16811486 | 2 |
| #20289748 | 2 |
| #20289746 | 2 |
| M32×Dic53 | 2 |
| #12009 | 53 |