Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
298 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20276961 | C2 | semidirect |
| 3. #20276760 | C2 | semidirect |
| 4. #20274205 | C2 | semidirect |
| 5. #20272768 | C2 | semidirect |
| 6. #20272674 | C2 | semidirect |
| 7. C53×#1333 | C2 | semidirect |
| 146. #1333 | D53 | semidirect |
| 172. C53 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287322 | 2 |
| #20276961 | 2 |
| #20276760 | 2 |
| #20274205 | 2 |
| #20272768 | 2 |
| #20272674 | 2 |
| C53×#1333 | 2 |
| #12350 | 53 |