Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20291067 | C2 | semidirect |
| 3. C2×#16811550 | C2 | semidirect |
| 5. #20289790 | C2 | semidirect |
| 6. #20289777 | C2 | semidirect |
| 25. #16810408 | C4 | semidirect |
| 26. #16810407 | C4 | semidirect |
| 27. #16810406 | C4 | semidirect |
| 28. C53×#350 | C4 | semidirect |
| 61. #13133157 | C2×C4 | semidirect |
| 63. C2×#11719908 | C2×C4 | semidirect |
| 68. M32×C53 | C2×C4 | semidirect |
| 69. C2×C16×C53 | C2×C4 | semidirect |
| 210. #350 | #6157 | semidirect |
| 212. C53 | #12926 | semidirect |
| 235. M32 | C2×#6157 | semidirect |
| 240. C2×C16 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291370 | 2 |
| #20291067 | 2 |
| C2×#16811550 | 2 |
| #20290604 | 2 |
| #20289790 | 2 |
| #20289777 | 2 |
| #350×D53 | 2 |
| #12926 | 53 |