Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20273478 | C2 | semidirect |
| 3. #20273316 | C2 | semidirect |
| 5. #20273070 | C2 | semidirect |
| 7. C8×M16×C53 | C2 | semidirect |
| 176. C8×M16 | D53 | semidirect |
| 205. C53 | #9789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810978 | 2 |
| #20273478 | 2 |
| #20273316 | 2 |
| #20273312 | 2 |
| #20273070 | 2 |
| #20273066 | 2 |
| C8×M16×C53 | 2 |
| #9789 | 53 |