Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 4. #20273266 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272579 | C2 | semidirect |
| 7. C53×#1515 | C2 | semidirect |
| 10. #16810971 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 43. C4×#88322 | C2×C4 | semidirect |
| 47. C4⋊Q8×C53 | C2×C4 | semidirect |
| 48. C4⋊Q8×C53 | C2×C4 | semidirect |
| 167. #1515 | D53 | semidirect |
| 192. C53 | #9425 | semidirect |
| 198. C4⋊Q8 | C4×D53 | semidirect |
| 199. C4⋊Q8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285091 | 2 |
| #20277891 | 2 |
| #20273428 | 2 |
| #20273266 | 2 |
| #20272581 | 2 |
| #20272579 | 2 |
| C53×#1515 | 2 |
| #9425 | 53 |