Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 2. #20291063 | C2 | semidirect |
| 4. #20290822 | C2 | semidirect |
| 5. #20289782 | C2 | semidirect |
| 6. #20289758 | C2 | semidirect |
| 27. #16810434 | C4 | semidirect |
| 28. #16810433 | C4 | semidirect |
| 29. #16810432 | C4 | semidirect |
| 30. C53×#360 | C4 | semidirect |
| 70. #13133157 | C2×C4 | semidirect |
| 74. #13133149 | C2×C4 | semidirect |
| 76. M32×C53 | C2×C4 | semidirect |
| 77. #106×C53 | C2×C4 | semidirect |
| 227. #360 | #6157 | semidirect |
| 229. C53 | #12951 | semidirect |
| 258. M32 | C2×#6157 | semidirect |
| 268. #106 | 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 |
| #20291063 | 2 |
| #20291043 | 2 |
| #20290822 | 2 |
| #20289782 | 2 |
| #20289758 | 2 |
| #20276449 | 2 |
| #12951 | 53 |