Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
774 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275550 | C2 | semidirect |
| 3. #20274659 | C2 | semidirect |
| 4. #20273230 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272601 | C2 | semidirect |
| 7. C53×#2341 | C2 | semidirect |
| 8. C2×#13133242 | C4 | semidirect |
| 14. #16810624 | C4 | semidirect |
| 155. Q8×C53 | #99 | semidirect |
| 230. #2341 | D53 | semidirect |
| 266. C53 | #9368 | semidirect |
| 393. Q8 | #13133131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283967 | 2 |
| #20275550 | 2 |
| #20274659 | 2 |
| #20273230 | 2 |
| #20272621 | 2 |
| #20272601 | 2 |
| C53×#2341 | 2 |
| #9368 | 53 |