Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
250 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 79 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×#16810460 | C2 | semidirect |
| 3. C4×#13133123 | C2 | semidirect |
| 4. C53×#2247 | C2 | semidirect |
| 19. #13133123 | D4 | semidirect |
| 60. C4×C53 | SD64 | semidirect |
| 64. #2247 | D53 | semidirect |
| 79. C53 | #13727 | semidirect |
| 125. C4 | #16810460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810460 | 2 |
| #20276965 | 2 |
| C4×#13133123 | 2 |
| C53×#2247 | 2 |
| #13727 | 53 |