Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20285116 | C2 | semidirect |
| 3. #20280583 | C2 | semidirect |
| 4. #20273341 | C2 | semidirect |
| 5. #20273263 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#1490 | C2 | semidirect |
| 202. #1490 | D53 | semidirect |
| 235. C53 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285116 | 2 |
| #20284806 | 2 |
| #20280583 | 2 |
| #20273341 | 2 |
| #20273263 | 2 |
| #20272580 | 2 |
| C53×#1490 | 2 |
| #10019 | 53 |