Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
984 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 335 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. #20275008 | C2 | semidirect |
| 2. #20274858 | C2 | semidirect |
| 17. #127×C53 | C8 | semidirect |
| 28. C2×D4×C53 | C2×C8 | semidirect |
| 39. C42×C53 | C2×C8 | semidirect |
| 83. C53 | #23355 | semidirect |
| 88. #127 | #88322 | semidirect |
| 100. C2×D4 | C2×#88322 | semidirect |
| 113. C42 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275008 | 2 |
| #20274858 | 2 |
| C4×#127×C53 | 2 |
| #23355 | 53 |