Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
654 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 184 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×#11719111 | C2 | semidirect |
| 2. #13131239 | C2 | direct (N × H) |
| 3. C2×#11718224 | C2 | semidirect |
| 4. C2×#11718281 | C2 | semidirect |
| 5. C2×#11718216 | C2 | semidirect |
| 11. #11719111 | C22 | semidirect |
| 15. C2×C13×Q32 | C4 | semidirect |
| 16. C2×#88068 | C4 | semidirect |
| 17. #11718580 | C4 | semidirect |
| 19. C2×D208 | C4 | semidirect |
| 21. #11718281 | C22 | semidirect |
| 22. #11718224 | C22 | semidirect |
| 23. #11718216 | C22 | semidirect |
| 48. C13×Q32 | C2×C4 | semidirect |
| 50. #88068 | C2×C4 | semidirect |
| 52. D208 | C2×C4 | semidirect |
| 126. C2×Q32 | #261 | semidirect |
| 167. Q32 | C2×#261 | semidirect |
| 182. C2×C13 | #2179 | semidirect |
| 222. C13 | C2×#2179 | semidirect |
| 263. C2 | #13131239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719111 | 2 |
| #13131239 | 2 |
| C2×#11718224 | 2 |
| C2×#11718281 | 2 |
| C2×#11718216 | 2 |
| C2×#11718580 | 2 |
| C2×#2179 | 13 |