Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #20276370 | C2 | semidirect |
| 5. #20275235 | C2 | semidirect |
| 6. #20275000 | C2 | semidirect |
| 7. C53×#1395 | C2 | semidirect |
| 195. #1395 | D53 | semidirect |
| 223. C53 | #13434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285588 | 2 |
| #20276386 | 2 |
| #20276370 | 2 |
| #20275260 | 2 |
| #20275235 | 2 |
| #20275000 | 2 |
| C53×#1395 | 2 |
| #13434 | 53 |