Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #20283741 | C2 | semidirect |
| 3. #20274700 | C2 | semidirect |
| 4. #20274647 | C2 | semidirect |
| 5. #20274645 | C2 | semidirect |
| 6. #20272582 | C2 | semidirect |
| 7. C53×#1289 | C2 | semidirect |
| 20. #16810541 | C4 | semidirect |
| 21. #16810533 | C4 | semidirect |
| 41. C22×#88322 | D4 | semidirect |
| 68. C22×C8×C53 | D4 | semidirect |
| 275. #1289 | D53 | semidirect |
| 308. C53 | #9472 | semidirect |
| 323. C22×C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283741 | 2 |
| #20278072 | 2 |
| #20274700 | 2 |
| #20274647 | 2 |
| #20274645 | 2 |
| #20272582 | 2 |
| C53×#1289 | 2 |
| #9472 | 53 |