Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 544 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. #20283432 | C2 | semidirect |
| 3. #20275514 | C2 | semidirect |
| 4. #20273362 | C2 | semidirect |
| 5. #20272610 | C2 | semidirect |
| 6. #20272559 | C2 | semidirect |
| 7. C53×#1486 | C2 | semidirect |
| 123. C2×#88322 | D8 | semidirect |
| 205. #1486 | D53 | semidirect |
| 236. C53 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284715 | 2 |
| #20283432 | 2 |
| #20275514 | 2 |
| #20273362 | 2 |
| #20272610 | 2 |
| #20272559 | 2 |
| C53×#1486 | 2 |
| #9049 | 53 |