Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20274707 | C2 | semidirect |
| 2. #20273473 | C2 | semidirect |
| 3. #20273392 | C2 | semidirect |
| 4. #20273166 | C2 | semidirect |
| 5. C2×D4⋊#88322 | C2 | semidirect |
| 6. #20272589 | C2 | semidirect |
| 229. C53 | #10456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274707 | 2 |
| #20273473 | 2 |
| #20273392 | 2 |
| #20273166 | 2 |
| C2×D4⋊#88322 | 2 |
| #20272589 | 2 |
| C53×#3036 | 2 |
| #10456 | 53 |