Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1350 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 447 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×D4×#88322 | C2 | semidirect |
| 2. #20275510 | C2 | semidirect |
| 3. #20274867 | C2 | semidirect |
| 4. C42×#88322 | C2 | semidirect |
| 24. C4×#88322 | D4 | semidirect |
| 27. #127×C53 | C8 | semidirect |
| 38. C2×D4×C53 | C2×C8 | semidirect |
| 48. C42×C53 | C2×C8 | semidirect |
| 73. #88322 | #127 | direct (N × H) |
| 83. C4×C53 | C8×D4 | semidirect |
| 106. C53 | C8×#127 | semidirect |
| 113. #127 | #88322 | direct (N × H) |
| 128. C2×D4 | C2×#88322 | semidirect |
| 143. C42 | C2×#88322 | semidirect |
| 172. C4 | D4×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#88322 | 2 |
| #20275510 | 2 |
| #20274867 | 2 |
| C42×#88322 | 2 |
| C4×#127×C53 | 2 |
| C8×#127 | 53 |