Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20290932 | C2 | semidirect |
| 4. #20290529 | C2 | semidirect |
| 5. #20289791 | C2 | semidirect |
| 6. #20289781 | C2 | semidirect |
| 13. #16811540 | C4 | semidirect |
| 14. #16811539 | C4 | semidirect |
| 15. #16811536 | C4 | semidirect |
| 16. #16811535 | C4 | semidirect |
| 22. #16810746 | C4 | semidirect |
| 23. #16810745 | C4 | semidirect |
| 24. #16810744 | C4 | semidirect |
| 30. C53×#444 | C4 | semidirect |
| 97. Q16×C53 | C42 | semidirect |
| 99. D8×C53 | C42 | semidirect |
| 117. Dic212 | C42 | semidirect |
| 118. D424 | C42 | semidirect |
| 218. #444 | #6157 | semidirect |
| 232. C53 | #12650 | semidirect |
| 296. Q16 | C4×#6157 | semidirect |
| 303. D8 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#360 | 2 |
| #20291023 | 2 |
| #20290932 | 2 |
| #20290529 | 2 |
| #20289791 | 2 |
| #20289781 | 2 |
| #444×D53 | 2 |
| #12650 | 53 |