Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20276504 | C2 | semidirect |
| 5. #20275459 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 21. #16810432 | C4 | semidirect |
| 49. #13133157 | C2×C4 | semidirect |
| 70. #106×C53 | C2×C4 | semidirect |
| 113. Dic212 | C4⋊C4 | semidirect |
| 115. D424 | C4⋊C4 | semidirect |
| 181. #1386 | 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 |
|---|---|
| #20283515 | 2 |
| #20276504 | 2 |
| C2×#16810432 | 2 |
| #20276428 | 2 |
| #20275459 | 2 |
| #20272798 | 2 |
| C53×#1386 | 2 |
| #12943 | 53 |