Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20276040 | C2 | semidirect |
| 3. #20275958 | C2 | semidirect |
| 4. #20272539 | C2 | semidirect |
| 5. #20272537 | C2 | semidirect |
| 225. C53 | #7765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281674 | 2 |
| #20276040 | 2 |
| #20275958 | 2 |
| #20272539 | 2 |
| #20272537 | 2 |
| #20272536 | 2 |
| C53×#2023 | 2 |
| #7765 | 53 |