Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 84 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. D53⋊#365 | C2 | semidirect |
| 4. #20290818 | C2 | semidirect |
| 5. #20289779 | C2 | semidirect |
| 6. #20289758 | C2 | semidirect |
| 27. #16810434 | C4 | semidirect |
| 28. #16810433 | C4 | semidirect |
| 29. #16810432 | C4 | semidirect |
| 30. C53×#360 | C4 | semidirect |
| 113. Q16×C53 | C4⋊C4 | semidirect |
| 115. D8×C53 | C4⋊C4 | semidirect |
| 125. Dic212 | C4⋊C4 | semidirect |
| 126. D424 | C4⋊C4 | semidirect |
| 231. #360 | #6157 | semidirect |
| 233. C53 | #12950 | semidirect |
| 297. Q16 | C4⋊#6157 | semidirect |
| 304. D8 | C4⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#443 | 2 |
| D53⋊#365 | 2 |
| D53⋊#360 | 2 |
| #20290818 | 2 |
| #20289779 | 2 |
| #20289758 | 2 |
| #360×D53 | 2 |
| #12950 | 53 |