Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
610 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 203 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×#11718344 | C2 | semidirect |
| 3. #13117068 | C2 | direct (N × H) |
| 4. C2×#11718095 | C2 | semidirect |
| 6. C2×C4×C13×C16 | C2 | semidirect |
| 19. #11718344 | C22 | semidirect |
| 20. C4×C13×C16 | C22 | semidirect |
| 22. #11718095 | C22 | semidirect |
| 86. C2×C4×C16 | D13 | semidirect |
| 125. C4×C16 | C2×D13 | semidirect |
| 165. C2×C13 | #2242 | semidirect |
| 199. C13 | C2×#2242 | semidirect |
| 236. C2 | #13117068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718344 | 2 |
| C2×#11718357 | 2 |
| #13117068 | 2 |
| C2×#11718095 | 2 |
| C2×#11718101 | 2 |
| C2×C4×C13×C16 | 2 |
| C2×#2242 | 13 |