Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 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. #135×#6157 | C2 | semidirect |
| 2. #20291036 | C2 | semidirect |
| 3. #20291029 | C2 | semidirect |
| 4. #20290868 | C2 | semidirect |
| 5. #20289796 | C2 | semidirect |
| 6. #20289758 | C2 | semidirect |
| 24. #16811066 | C4 | semidirect |
| 25. #16811063 | C4 | semidirect |
| 27. #16811059 | C4 | semidirect |
| 32. C53×#509 | C4 | semidirect |
| 67. C2×Dic212 | C2×C4 | semidirect |
| 79. #13133157 | C2×C4 | semidirect |
| 83. C2×D8×C53 | C2×C4 | semidirect |
| 86. M32×C53 | C2×C4 | semidirect |
| 234. #509 | #6157 | semidirect |
| 251. C53 | #13027 | semidirect |
| 269. C2×D8 | C2×#6157 | semidirect |
| 292. M32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#6157 | 2 |
| #20291036 | 2 |
| #20291029 | 2 |
| #20290868 | 2 |
| #20289796 | 2 |
| #20289758 | 2 |
| #20287847 | 2 |
| #13027 | 53 |