Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20290310 | C2 | semidirect |
| 3. #20289739 | C2 | semidirect |
| 4. #20289676 | C2 | semidirect |
| 6. #20289631 | C2 | semidirect |
| 36. #13133162 | C8 | semidirect |
| 61. Dic212 | C2×C8 | semidirect |
| 65. C16×C53 | C2×C8 | semidirect |
| 125. C53 | #12065 | semidirect |
| 169. C16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290313 | 2 |
| #20290310 | 2 |
| #20289739 | 2 |
| #20289676 | 2 |
| #20289674 | 2 |
| #20289631 | 2 |
| #20276578 | 2 |
| #12065 | 53 |