Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291063 | C2 | semidirect |
| 3. C2×#16811548 | C2 | semidirect |
| 5. #20289787 | C2 | semidirect |
| 6. #20289783 | C2 | semidirect |
| 25. #16810408 | C4 | semidirect |
| 26. #16810407 | C4 | semidirect |
| 27. #16810406 | C4 | semidirect |
| 28. C53×#350 | C4 | semidirect |
| 61. #13133157 | C2×C4 | semidirect |
| 65. C2×#11719908 | C2×C4 | semidirect |
| 68. M32×C53 | C2×C4 | semidirect |
| 69. C2×C16×C53 | C2×C4 | semidirect |
| 206. #350 | #6157 | semidirect |
| 208. C53 | #12934 | semidirect |
| 233. M32 | C2×#6157 | semidirect |
| 236. C2×C16 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291369 | 2 |
| #20291063 | 2 |
| C2×#16811548 | 2 |
| #20290601 | 2 |
| #20289787 | 2 |
| #20289783 | 2 |
| #20276341 | 2 |
| #12934 | 53 |