Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
572 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 100 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×#13133285 | C2 | semidirect |
| 2. C2×#16811539 | C2 | semidirect |
| 3. #20290943 | C2 | semidirect |
| 4. #20289786 | C2 | semidirect |
| 17. #16810865 | C4 | semidirect |
| 18. #16810864 | C4 | semidirect |
| 19. #16810856 | C4 | semidirect |
| 24. C53×#466 | C4 | semidirect |
| 35. #13133285 | D4 | semidirect |
| 40. C2×Dic212 | C2×C4 | semidirect |
| 57. #13133151 | C2×C4 | semidirect |
| 62. C2×D8×C53 | C2×C4 | semidirect |
| 65. #107×C53 | C2×C4 | semidirect |
| 174. C22×C53 | #360 | semidirect |
| 182. C2×D53 | #360 | semidirect |
| 216. #466 | #6157 | semidirect |
| 227. C53 | #13001 | semidirect |
| 235. C2×D8 | C2×#6157 | semidirect |
| 261. #107 | C2×#6157 | semidirect |
| 385. C22 | #16811539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133285 | 2 |
| C2×#16811539 | 2 |
| #20290943 | 2 |
| #20289786 | 2 |
| #20284294 | 2 |
| #13001 | 53 |