Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20276501 | C2 | semidirect |
| 5. #20272822 | C2 | semidirect |
| 6. #20272799 | C2 | semidirect |
| 7. C53×#1944 | C2 | semidirect |
| 20. #16810432 | C4 | semidirect |
| 48. #13133157 | C2×C4 | semidirect |
| 67. #106×C53 | C2×C4 | semidirect |
| 113. Dic212 | C4⋊C4 | semidirect |
| 115. D424 | C4⋊C4 | semidirect |
| 180. #1944 | D53 | semidirect |
| 209. C53 | #12943 | semidirect |
| 245. #106 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283517 | 2 |
| #20276501 | 2 |
| C2×#16810432 | 2 |
| #20276425 | 2 |
| #20272822 | 2 |
| #20272799 | 2 |
| C53×#1944 | 2 |
| #12943 | 53 |