Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 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 |
|---|---|---|
| 1. #20286098 | C2 | semidirect |
| 3. #20273855 | C2 | semidirect |
| 4. #20273836 | C2 | semidirect |
| 5. #20273793 | C2 | semidirect |
| 6. #20273774 | C2 | semidirect |
| 7. #20273450 | C2 | semidirect |
| 8. #20273170 | C2 | semidirect |
| 9. C53×#3550 | C2 | semidirect |
| 186. #3550 | D53 | semidirect |
| 227. C53 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286098 | 2 |
| #20285141 | 2 |
| #20273855 | 2 |
| #20273836 | 2 |
| #20273793 | 2 |
| #20273774 | 2 |
| #20273450 | 2 |
| #20273170 | 2 |
| C53×#3550 | 2 |
| #18688 | 53 |