Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×#13133286 | C2 | semidirect |
| 2. C2×#16811535 | C2 | semidirect |
| 3. D53⋊(C22⋊C16) | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 17. #16810860 | C4 | semidirect |
| 18. #16810859 | C4 | semidirect |
| 21. #16810856 | C4 | semidirect |
| 24. C53×#466 | C4 | semidirect |
| 35. #13133286 | D4 | semidirect |
| 39. C2×D424 | C2×C4 | semidirect |
| 57. #13133151 | C2×C4 | semidirect |
| 62. C2×D8×C53 | C2×C4 | semidirect |
| 65. #107×C53 | C2×C4 | semidirect |
| 186. C22×C53 | #357 | semidirect |
| 201. C2×D53 | #357 | semidirect |
| 243. #466 | #6157 | semidirect |
| 252. C53 | #12991 | semidirect |
| 261. C2×D8 | C2×#6157 | semidirect |
| 290. #107 | C2×#6157 | semidirect |
| 433. C22 | #16811535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133286 | 2 |
| C2×#16811535 | 2 |
| D53⋊(C22⋊C16) | 2 |
| #20289772 | 2 |
| #466×D53 | 2 |
| #12991 | 53 |