Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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. #13133210 | C2 | direct (N × H) |
| 2. C2×C4⋊Dic53 | C2 | semidirect |
| 3. C2×#11719919 | C2 | semidirect |
| 4. C2×#11719919 | C2 | semidirect |
| 7. C2×C4×Dic53 | C2 | semidirect |
| 19. C4⋊Dic53 | C22 | semidirect |
| 20. #11719919 | C22 | semidirect |
| 21. #11719919 | C22 | semidirect |
| 22. C4×Dic53 | C22 | semidirect |
| 55. C2×C53 | #126 | semidirect |
| 60. C53 | C2×#126 | semidirect |
| 115. C2 | #13133210 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133210 | 2 |
| C2×C4⋊Dic53 | 2 |
| C2×#11719919 | 2 |
| C2×C22⋊Dic53 | 2 |
| C2×C4×Dic53 | 2 |
| C2×C22⋊C4×C53 | 2 |
| C2×#126 | 53 |