Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1092 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20275556 | C2 | semidirect |
| 3. #20273448 | C2 | semidirect |
| 4. #20273306 | C2 | semidirect |
| 5. #20273155 | C2 | semidirect |
| 6. #20273152 | C2 | semidirect |
| 7. C53×#1965 | C2 | semidirect |
| 21. #16810647 | C22 | semidirect |
| 23. C4×#11719917 | C22 | semidirect |
| 32. C53×#423 | C22 | semidirect |
| 34. C4×M16×C53 | C22 | semidirect |
| 226. D212 | #100 | semidirect |
| 236. Dic106 | #100 | semidirect |
| 272. #1965 | D53 | semidirect |
| 299. #423 | C2×D53 | semidirect |
| 303. C4×M16 | C2×D53 | semidirect |
| 311. C53 | #8469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288491 | 2 |
| #20275556 | 2 |
| #20273448 | 2 |
| #20273306 | 2 |
| #20273155 | 2 |
| #20273152 | 2 |
| C53×#1965 | 2 |
| #8469 | 53 |