Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20287724 | C2 | semidirect |
| 2. #20276980 | C2 | semidirect |
| 3. #20276779 | C2 | semidirect |
| 4. #20276767 | C2 | semidirect |
| 5. #20276748 | C2 | semidirect |
| 6. #20276623 | C2 | semidirect |
| 7. #20276580 | C2 | semidirect |
| 8. C4×D848 | C2 | semidirect |
| 9. C53×#2249 | C2 | semidirect |
| 147. #2249 | D53 | semidirect |
| 184. C53 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287724 | 2 |
| #20276980 | 2 |
| #20276779 | 2 |
| #20276767 | 2 |
| #20276748 | 2 |
| #20276623 | 2 |
| #20276580 | 2 |
| C4×D848 | 2 |
| C53×#2249 | 2 |
| #33970 | 53 |