Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20291474 | C2 | semidirect |
| 2. #20291036 | C2 | semidirect |
| 3. #20291024 | C2 | semidirect |
| 4. #20290872 | C2 | semidirect |
| 5. #20289783 | C2 | semidirect |
| 6. #20289764 | C2 | semidirect |
| 24. C2×#13133162 | C4 | semidirect |
| 25. C2×#13133161 | C4 | semidirect |
| 26. C2×#13133158 | C4 | semidirect |
| 28. C2×D16×C53 | C4 | semidirect |
| 54. C2×Dic212 | C2×C4 | semidirect |
| 68. C2×#11719908 | C2×C4 | semidirect |
| 70. C2×D8×C53 | C2×C4 | semidirect |
| 72. C2×C16×C53 | C2×C4 | semidirect |
| 205. C2×D16 | #6157 | semidirect |
| 218. C53 | #13033 | semidirect |
| 234. C2×D8 | C2×#6157 | semidirect |
| 253. C2×C16 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291474 | 2 |
| #20291036 | 2 |
| #20291024 | 2 |
| #20290872 | 2 |
| #20289783 | 2 |
| #20289764 | 2 |
| C2×#16811057 | 2 |
| #13033 | 53 |