Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
840 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20277068 | C2 | semidirect |
| 3. #20273232 | C2 | semidirect |
| 4. #20272600 | C2 | semidirect |
| 5. C53×#1462 | C2 | semidirect |
| 10. #16810559 | C4 | semidirect |
| 11. #16810532 | C4 | semidirect |
| 21. C22×D212 | C2×C4 | semidirect |
| 29. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 42. #13133124 | C2×C4 | semidirect |
| 43. #13133124 | D4 | semidirect |
| 184. #1462 | D53 | semidirect |
| 209. C53 | #9409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279646 | 2 |
| #20277068 | 2 |
| #20273232 | 2 |
| #20272600 | 2 |
| C53×#1462 | 2 |
| #9409 | 53 |