Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#11718580 | C2 | semidirect |
| 2. #13117146 | C2 | direct (N × H) |
| 3. C2×#11718113 | C2 | semidirect |
| 4. C2×D416 | C2 | semidirect |
| 5. C2×D13×C32 | C2 | semidirect |
| 6. C2×C13×Q64 | C2 | semidirect |
| 11. #11718580 | C22 | semidirect |
| 14. C13×Q64 | C22 | semidirect |
| 16. #11718113 | C22 | semidirect |
| 18. D416 | C22 | semidirect |
| 19. D13×C32 | C22 | semidirect |
| 60. C2×Q64 | D13 | semidirect |
| 87. Q64 | C2×D13 | semidirect |
| 120. C2×C13 | #2262 | semidirect |
| 143. C13 | C2×#2262 | semidirect |
| 171. C2 | #13117146 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718580 | 2 |
| #13117146 | 2 |
| C2×#11718113 | 2 |
| C2×D416 | 2 |
| C2×D13×C32 | 2 |
| C2×C13×Q64 | 2 |
| C2×#2262 | 13 |