Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
882 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 197 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. #20275011 | C2 | semidirect |
| 3. #20275011 | C2 | semidirect |
| 4. #20275011 | C2 | semidirect |
| 5. #20275006 | C2 | semidirect |
| 6. #20274860 | C2 | semidirect |
| 7. C53×#1840 | C2 | semidirect |
| 154. #1840 | D53 | semidirect |
| 177. C53 | #23359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277996 | 2 |
| #20275011 | 2 |
| #20275006 | 2 |
| #20274860 | 2 |
| C53×#1840 | 2 |
| #23359 | 53 |