Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275543 | C2 | semidirect |
| 3. #20274867 | C2 | semidirect |
| 4. #20273393 | C2 | semidirect |
| 5. #20273392 | C2 | semidirect |
| 6. #20272589 | C2 | semidirect |
| 7. C53×#1962 | C2 | semidirect |
| 109. C42×C53 | D8 | semidirect |
| 203. #1962 | D53 | semidirect |
| 236. C53 | #10518 | semidirect |
| 329. C42 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286022 | 2 |
| #20275543 | 2 |
| #20274867 | 2 |
| #20273393 | 2 |
| #20273392 | 2 |
| #20272589 | 2 |
| C53×#1962 | 2 |
| #10518 | 53 |