Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #20284810 | C2 | semidirect |
| 3. #20273350 | C2 | semidirect |
| 4. #20273188 | C2 | semidirect |
| 5. #20273055 | C2 | semidirect |
| 6. #20272578 | C2 | semidirect |
| 7. C53×#3235 | C2 | semidirect |
| 190. #3235 | D53 | semidirect |
| 228. C53 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20284711 | 2 |
| #20273350 | 2 |
| #20273188 | 2 |
| #20273055 | 2 |
| #20272578 | 2 |
| C53×#3235 | 2 |
| #10042 | 53 |