Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20291048 | C2 | semidirect |
| 3. #20290654 | C2 | semidirect |
| 4. #20289789 | C2 | semidirect |
| 167. C4×C53 | #361 | semidirect |
| 205. C53 | #12818 | semidirect |
| 353. C4 | #16811541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291048 | 2 |
| C2×#16811541 | 2 |
| #20290654 | 2 |
| #20289789 | 2 |
| C4×D8×D53 | 2 |
| #12818 | 53 |