Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
922 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 219 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. #20276129 | C2 | semidirect |
| 3. #20275520 | C2 | semidirect |
| 4. #20275037 | C2 | semidirect |
| 5. #20274842 | C2 | semidirect |
| 6. C4×C22⋊#88322 | C2 | semidirect |
| 7. C53×#2285 | C2 | semidirect |
| 146. #2285 | D53 | semidirect |
| 176. C53 | #27974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283060 | 2 |
| #20276129 | 2 |
| #20275520 | 2 |
| #20275037 | 2 |
| #20274842 | 2 |
| C4×C22⋊#88322 | 2 |
| C53×#2285 | 2 |
| #27974 | 53 |