Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1054 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20275510 | C2 | semidirect |
| 3. #20273393 | C2 | semidirect |
| 4. #20273165 | C2 | semidirect |
| 5. C53×#1800 | C2 | semidirect |
| 14. C2×C4⋊#88322 | C22 | semidirect |
| 16. C2×C4×#88322 | C22 | semidirect |
| 21. C53×#423 | C22 | semidirect |
| 187. #1800 | D53 | semidirect |
| 206. #423 | C2×D53 | semidirect |
| 215. C53 | #8353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288479 | 2 |
| #20275510 | 2 |
| #20273393 | 2 |
| #20273165 | 2 |
| C53×#1800 | 2 |
| #8353 | 53 |