Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
642 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20285630 | C2 | semidirect |
| 2. #20285168 | C2 | semidirect |
| 3. #20275554 | C2 | semidirect |
| 4. #20273307 | C2 | semidirect |
| 5. #20273132 | C2 | semidirect |
| 6. #20272604 | C2 | semidirect |
| 7. C53×#3253 | C2 | semidirect |
| 197. #3253 | D53 | semidirect |
| 234. C53 | #10104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20285168 | 2 |
| #20275554 | 2 |
| #20273307 | 2 |
| #20273132 | 2 |
| #20272604 | 2 |
| C53×#3253 | 2 |
| #10104 | 53 |