Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275498 | C2 | semidirect |
| 5. #20272823 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C2×C53×#366 | C2 | semidirect |
| 18. #16810431 | C4 | semidirect |
| 46. #13133153 | C2×C4 | semidirect |
| 58. C2×C16×C53 | C2×C4 | semidirect |
| 155. C2×#366 | D53 | semidirect |
| 185. C53 | #12945 | semidirect |
| 210. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283589 | 2 |
| C2×#16810431 | 2 |
| #20276425 | 2 |
| #20275498 | 2 |
| #20272823 | 2 |
| #20272803 | 2 |
| C2×C53×#366 | 2 |
| #12945 | 53 |