Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 1. #13133216 | C2 | semidirect |
| 2. #13133207 | C2 | semidirect |
| 3. #13133197 | C2 | semidirect |
| 4. #13133196 | C2 | semidirect |
| 5. #13133196 | C2 | semidirect |
| 6. #13133195 | C2 | semidirect |
| 7. #13133182 | C2 | semidirect |
| 10. C4⋊C4×D53 | C2 | semidirect |
| 11. C2×C4⋊C4×C53 | C2 | semidirect |
| 43. C22⋊D53 | Q8 | semidirect |
| 75. C53 | #554 | semidirect |
| 86. C2×C4⋊C4 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133216 | 2 |
| #13133207 | 2 |
| #13133197 | 2 |
| #13133196 | 2 |
| #13133195 | 2 |
| #13133182 | 2 |
| C4×C22⋊D53 | 2 |
| C4⋊C4×D53 | 2 |
| C2×C4⋊C4×C53 | 2 |
| #554 | 53 |