Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20286067 | C2 | semidirect |
| 2. #20276646 | C2 | semidirect |
| 4. #20276026 | C2 | semidirect |
| 5. #20272728 | C2 | semidirect |
| 6. #20272725 | C2 | semidirect |
| 7. C53×#1322 | C2 | semidirect |
| 180. #1322 | D53 | semidirect |
| 207. C53 | #12160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286067 | 2 |
| #20276646 | 2 |
| #20276629 | 2 |
| #20276026 | 2 |
| #20272728 | 2 |
| #20272725 | 2 |
| C53×#1322 | 2 |
| #12160 | 53 |