Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291376 | C2 | semidirect |
| 2. D53⋊#361 | C2 | semidirect |
| 3. C2×#16811541 | C2 | semidirect |
| 4. #20290958 | C2 | semidirect |
| 5. #20289792 | C2 | semidirect |
| 6. #20289784 | C2 | semidirect |
| 261. C53 | #13007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291376 | 2 |
| D53⋊#361 | 2 |
| C2×#16811541 | 2 |
| #20290958 | 2 |
| #20289792 | 2 |
| #20289784 | 2 |
| #472×D53 | 2 |
| #13007 | 53 |