Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20277874 | C2 | semidirect |
| 3. #20275552 | C2 | semidirect |
| 4. #20273232 | C2 | semidirect |
| 5. #20272620 | C2 | semidirect |
| 6. #20272567 | C2 | semidirect |
| 7. C53×#1510 | C2 | semidirect |
| 9. #16810941 | C4 | semidirect |
| 12. #16810757 | C4 | semidirect |
| 58. C22⋊#88322 | C2×C4 | semidirect |
| 64. C22×D4×C53 | C2×C4 | semidirect |
| 71. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 243. #1510 | D53 | semidirect |
| 279. C53 | #9343 | semidirect |
| 283. C22×D4 | C4×D53 | semidirect |
| 300. C2×C4⋊C4 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285512 | 2 |
| #20277874 | 2 |
| #20275552 | 2 |
| #20273232 | 2 |
| #20272620 | 2 |
| #20272567 | 2 |
| C53×#1510 | 2 |
| #9343 | 53 |