Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276469 | C2 | semidirect |
| 3. #20273477 | C2 | semidirect |
| 4. #20272770 | C2 | semidirect |
| 5. #20272762 | C2 | semidirect |
| 6. #20272760 | C2 | semidirect |
| 7. C53×#1364 | C2 | semidirect |
| 137. #1364 | D53 | semidirect |
| 162. C53 | #11985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285295 | 2 |
| #20276469 | 2 |
| #20273477 | 2 |
| #20272770 | 2 |
| #20272762 | 2 |
| #20272760 | 2 |
| C53×#1364 | 2 |
| #11985 | 53 |