Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. C2×#16811552 | C2 | semidirect |
| 2. #20291066 | C2 | semidirect |
| 4. #20289796 | C2 | semidirect |
| 16. #16811041 | C4 | semidirect |
| 17. #16811040 | C4 | semidirect |
| 19. #16811039 | C4 | semidirect |
| 24. C53×#504 | C4 | semidirect |
| 166. #504 | #6157 | semidirect |
| 179. C53 | #12841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811552 | 2 |
| #20291066 | 2 |
| #20290602 | 2 |
| #20289796 | 2 |
| #504×D53 | 2 |
| #12841 | 53 |