Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #20283854 | C2 | semidirect |
| 3. #20275513 | C2 | semidirect |
| 4. #20273159 | C2 | semidirect |
| 5. #20272614 | C2 | semidirect |
| 6. #20272566 | C2 | semidirect |
| 7. C53×#1524 | C2 | semidirect |
| 224. #1524 | D53 | semidirect |
| 262. C53 | #9052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284758 | 2 |
| #20283854 | 2 |
| #20275513 | 2 |
| #20273159 | 2 |
| #20272614 | 2 |
| #20272566 | 2 |
| C53×#1524 | 2 |
| #9052 | 53 |