Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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. C16×D212 | C2 | semidirect |
| 2. #20274101 | C2 | semidirect |
| 4. #20272787 | C2 | semidirect |
| 5. #20272770 | C2 | semidirect |
| 6. #20272761 | C2 | semidirect |
| 7. C53×#2240 | C2 | semidirect |
| 109. #2240 | D53 | semidirect |
| 136. C53 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D212 | 2 |
| #20274101 | 2 |
| #20274067 | 2 |
| #20272787 | 2 |
| #20272770 | 2 |
| #20272761 | 2 |
| C53×#2240 | 2 |
| #12467 | 53 |