Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
822 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20285933 | C2 | semidirect |
| 2. C2×#16810993 | C2 | semidirect |
| 3. #20274049 | C2 | semidirect |
| 4. #20274043 | C2 | semidirect |
| 5. #20274038 | C2 | semidirect |
| 6. #20273342 | C2 | semidirect |
| 7. #20273335 | C2 | semidirect |
| 238. C53 | #19060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285933 | 2 |
| C2×#16810993 | 2 |
| #20274049 | 2 |
| #20274043 | 2 |
| #20274038 | 2 |
| #20273342 | 2 |
| #20273335 | 2 |
| C53×#3553 | 2 |
| #19060 | 53 |