Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283434 | C2 | semidirect |
| 3. #20273365 | C2 | semidirect |
| 4. #20273140 | C2 | semidirect |
| 5. #20272612 | C2 | semidirect |
| 6. #20272560 | C2 | semidirect |
| 7. C53×#1955 | C2 | semidirect |
| 105. C2×C8×C53 | D8 | semidirect |
| 203. #1955 | D53 | semidirect |
| 236. C53 | #9049 | semidirect |
| 321. C2×C8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284715 | 2 |
| #20283434 | 2 |
| #20273365 | 2 |
| #20273140 | 2 |
| #20272612 | 2 |
| #20272560 | 2 |
| C53×#1955 | 2 |
| #9049 | 53 |