Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #20290930 | C2 | semidirect |
| 4. #20290531 | C2 | semidirect |
| 5. #20289790 | C2 | semidirect |
| 6. #20289779 | C2 | semidirect |
| 10. #16811670 | C4 | semidirect |
| 11. #16811670 | C4 | semidirect |
| 12. #16811669 | C4 | semidirect |
| 13. #16811669 | C4 | semidirect |
| 21. #16811536 | C4 | semidirect |
| 22. #16811535 | C4 | semidirect |
| 29. #16810434 | C4 | semidirect |
| 30. #16810433 | C4 | semidirect |
| 31. #16810432 | C4 | semidirect |
| 32. C53×#360 | C4 | semidirect |
| 118. Q16×C53 | C42 | semidirect |
| 120. D8×C53 | C42 | semidirect |
| 130. Dic212 | C42 | semidirect |
| 131. D424 | C42 | semidirect |
| 236. #360 | #6157 | semidirect |
| 242. C53 | #12650 | semidirect |
| 308. Q16 | C4×#6157 | semidirect |
| 315. D8 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#444 | 2 |
| #20291023 | 2 |
| #20290930 | 2 |
| #20290531 | 2 |
| #20289790 | 2 |
| #20289779 | 2 |
| #360×D53 | 2 |
| #12650 | 53 |