Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1318 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20283158 | C2 | semidirect |
| 3. #20275182 | C2 | semidirect |
| 4. #20275177 | C2 | semidirect |
| 5. #20274795 | C2 | semidirect |
| 6. #20274641 | C2 | semidirect |
| 7. C53×#1821 | C2 | semidirect |
| 183. #1821 | D53 | semidirect |
| 210. C53 | #21757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811204 | 2 |
| #20283158 | 2 |
| #20275182 | 2 |
| #20275177 | 2 |
| #20274795 | 2 |
| #20274641 | 2 |
| C53×#1821 | 2 |
| #21757 | 53 |