Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20274798 | C2 | semidirect |
| 3. #20272722 | C2 | semidirect |
| 4. #20272719 | C2 | semidirect |
| 5. C53×#1464 | C2 | semidirect |
| 178. #1464 | D53 | semidirect |
| 205. C53 | #11804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277951 | 2 |
| #20274798 | 2 |
| #20272722 | 2 |
| #20272719 | 2 |
| C53×#1464 | 2 |
| #11804 | 53 |