Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #13133212 | C2 | semidirect |
| 2. #13133208 | C2 | semidirect |
| 3. #13133206 | C2 | semidirect |
| 4. #13133202 | C2 | semidirect |
| 5. #13133193 | C2 | semidirect |
| 7. C4×D212 | C2 | semidirect |
| 8. C4×D212 | C2 | semidirect |
| 9. #13133174 | C2 | semidirect |
| 10. C42×D53 | C2 | semidirect |
| 11. C4×Q8×C53 | C2 | semidirect |
| 75. C53 | #529 | semidirect |
| 82. C4×Q8 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133212 | 2 |
| #13133208 | 2 |
| #13133206 | 2 |
| #13133202 | 2 |
| #13133193 | 2 |
| #13133192 | 2 |
| C4×D212 | 2 |
| #13133174 | 2 |
| C42×D53 | 2 |
| C4×Q8×C53 | 2 |
| #529 | 53 |