Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20276997 | C2 | semidirect |
| 3. #20276993 | C2 | semidirect |
| 4. #20276988 | C2 | semidirect |
| 7. C53×#2254 | C2 | semidirect |
| 35. C16×D53 | Q8 | semidirect |
| 100. #2254 | D53 | semidirect |
| 124. C53 | #33726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285226 | 2 |
| #20276997 | 2 |
| #20276993 | 2 |
| #20276988 | 2 |
| #20276498 | 2 |
| C4×C16×D53 | 2 |
| C53×#2254 | 2 |
| #33726 | 53 |