Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1618 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 267 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. C2×#16811013 | C2 | semidirect |
| 2. C2×#16811010 | C2 | semidirect |
| 3. C2×#16811005 | C2 | semidirect |
| 4. C2×#16810999 | C2 | semidirect |
| 5. #20280821 | C2 | semidirect |
| 6. #20274402 | C2 | semidirect |
| 7. C53×#2657 | C2 | semidirect |
| 46. #13133128 | D4 | semidirect |
| 47. C4×#88322 | D4 | semidirect |
| 138. #2657 | D53 | semidirect |
| 162. C53 | #33308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811013 | 2 |
| C2×#16811010 | 2 |
| C2×#16811005 | 2 |
| C2×#16810999 | 2 |
| #20280821 | 2 |
| #20274402 | 2 |
| C53×#2657 | 2 |
| #33308 | 53 |