Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #13133211 | C2 | semidirect |
| 2. #13133209 | C2 | semidirect |
| 3. #13133205 | C2 | semidirect |
| 4. #13133200 | C2 | semidirect |
| 5. #13133196 | C2 | semidirect |
| 7. C4×Dic106 | C2 | semidirect |
| 8. C4×D212 | C2 | semidirect |
| 9. C4×C22⋊D53 | C2 | semidirect |
| 10. #13133174 | C2 | semidirect |
| 11. C2×C42×C53 | C2 | semidirect |
| 75. C53 | #529 | semidirect |
| 86. C2×C42 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133211 | 2 |
| #13133209 | 2 |
| #13133205 | 2 |
| #13133200 | 2 |
| #13133196 | 2 |
| #13133191 | 2 |
| C4×Dic106 | 2 |
| C4×D212 | 2 |
| C4×C22⋊D53 | 2 |
| #13133174 | 2 |
| C2×C42×C53 | 2 |
| #529 | 53 |