Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C2×#16810437 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20276444 | C2 | semidirect |
| 5. #20276432 | C2 | semidirect |
| 6. #20274839 | C2 | semidirect |
| 7. C53×#2110 | C2 | semidirect |
| 13. #16811007 | C4 | semidirect |
| 14. #16811000 | C4 | semidirect |
| 62. M32×C53 | D4 | semidirect |
| 64. C2×C16×C53 | D4 | semidirect |
| 174. #2110 | D53 | semidirect |
| 201. C53 | #13215 | semidirect |
| 233. M32 | D212 | semidirect |
| 235. C2×C16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285201 | 2 |
| C2×#16810437 | 2 |
| #20276452 | 2 |
| #20276444 | 2 |
| #20276432 | 2 |
| #20274839 | 2 |
| C53×#2110 | 2 |
| #13215 | 53 |