Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 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. #20276488 | C2 | semidirect |
| 5. #20275463 | C2 | semidirect |
| 6. #20272817 | C2 | semidirect |
| 7. C53×#1376 | C2 | semidirect |
| 21. #16810434 | C4 | semidirect |
| 46. #13133149 | C2×C4 | semidirect |
| 57. M32×C53 | C2×C4 | semidirect |
| 156. #1376 | D53 | semidirect |
| 180. C53 | #12951 | semidirect |
| 203. M32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133239 | 2 |
| #20276488 | 2 |
| #20276465 | 2 |
| #20276452 | 2 |
| #20275463 | 2 |
| #20272817 | 2 |
| C53×#1376 | 2 |
| #12951 | 53 |