Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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. Q8×Dic53 | C2 | semidirect |
| 4. #13133148 | C2 | semidirect |
| 6. C8×Dic53 | C2 | semidirect |
| 7. #103×C53 | C2 | semidirect |
| 13. #11719924 | C4 | semidirect |
| 22. Q8×C53 | C2×C4 | semidirect |
| 33. #88322 | C2×C4 | semidirect |
| 44. Dic53 | SD16 | semidirect |
| 50. C53 | C4×SD16 | semidirect |
| 55. #103 | D53 | semidirect |
| 72. Q8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719924 | 2 |
| Q8×Dic53 | 2 |
| #13133179 | 2 |
| #13133148 | 2 |
| #13133139 | 2 |
| C8×Dic53 | 2 |
| #103×C53 | 2 |
| C4×SD16 | 53 |