Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #13127974 | C2 | semidirect |
| 2. C2×#11718111 | C2 | semidirect |
| 3. #13116953 | C2 | semidirect |
| 4. #13113027 | C2 | semidirect |
| 5. #13113020 | C2 | semidirect |
| 6. #13112979 | C2 | semidirect |
| 7. C13×#2263 | C2 | semidirect |
| 10. C2×C13×D16 | C22 | semidirect |
| 20. C13×M64 | C22 | semidirect |
| 23. #11718098 | C22 | semidirect |
| 24. C2×#88034 | C22 | semidirect |
| 82. #2263 | D13 | semidirect |
| 118. C2×D16 | C2×D13 | semidirect |
| 124. M64 | C2×D13 | semidirect |
| 201. C13 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127974 | 2 |
| C2×#11718111 | 2 |
| #13116953 | 2 |
| #13113027 | 2 |
| #13113020 | 2 |
| #13112979 | 2 |
| C13×#2263 | 2 |
| #13669 | 13 |