Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 2. C2×#16811536 | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 17. #16810865 | C4 | semidirect |
| 18. #16810864 | C4 | semidirect |
| 21. #16810861 | C4 | semidirect |
| 24. C53×#467 | C4 | semidirect |
| 38. C2×Dic212 | C2×C4 | semidirect |
| 57. #13133151 | C2×C4 | semidirect |
| 62. C2×Q16×C53 | C2×C4 | semidirect |
| 65. #107×C53 | C2×C4 | semidirect |
| 173. C22×C53 | #358 | semidirect |
| 181. C2×D53 | #358 | semidirect |
| 223. #467 | #6157 | semidirect |
| 232. C53 | #12993 | semidirect |
| 240. C2×Q16 | C2×#6157 | semidirect |
| 270. #107 | C2×#6157 | semidirect |
| 393. C22 | #16811536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133286 | 2 |
| C2×#16811536 | 2 |
| D53⋊(C22⋊C16) | 2 |
| #20289772 | 2 |
| #467×D53 | 2 |
| #12993 | 53 |