Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
880 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20274635 | C2 | semidirect |
| 3. #20273053 | C2 | semidirect |
| 4. #20272620 | C2 | semidirect |
| 5. C53×#2973 | C2 | semidirect |
| 45. C2×M16×C53 | D4 | semidirect |
| 116. C23×C53 | #100 | semidirect |
| 190. #2973 | D53 | semidirect |
| 220. C53 | #9503 | semidirect |
| 232. C2×M16 | C22⋊D53 | semidirect |
| 327. C23 | #13133133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278071 | 2 |
| #20274635 | 2 |
| #20273053 | 2 |
| #20272620 | 2 |
| C53×#2973 | 2 |
| #9503 | 53 |