Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20277886 | C2 | semidirect |
| 3. #20275540 | C2 | semidirect |
| 4. C2×#16810362 | C2 | semidirect |
| 5. #20272597 | C2 | semidirect |
| 6. #20272596 | C2 | semidirect |
| 7. C53×#1961 | C2 | semidirect |
| 12. #16811010 | C4 | semidirect |
| 59. #13133128 | C2×C4 | semidirect |
| 71. #127×C53 | C2×C4 | semidirect |
| 246. #1961 | D53 | semidirect |
| 281. C53 | #9001 | semidirect |
| 300. #127 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811010 | 2 |
| #20277886 | 2 |
| #20275540 | 2 |
| C2×#16810362 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1961 | 2 |
| #9001 | 53 |