Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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. C22×D208 | C2 | semidirect |
| 2. #13117148 | C2 | direct (N × H) |
| 3. C2×#11718113 | C2 | semidirect |
| 4. C2×#11718111 | C2 | semidirect |
| 5. C2×#11718091 | C2 | semidirect |
| 6. C2×C13×#508 | C2 | semidirect |
| 10. C13×#508 | C22 | semidirect |
| 11. C2×C13×Q32 | C22 | semidirect |
| 13. C2×C13×D16 | C22 | semidirect |
| 18. C2×D208 | C22 | semidirect |
| 19. #11718113 | C22 | semidirect |
| 20. #11718111 | C22 | semidirect |
| 21. #11718091 | C22 | semidirect |
| 22. C2×#88034 | C22 | semidirect |
| 36. C13×Q32 | C23 | semidirect |
| 39. C13×D16 | C23 | semidirect |
| 47. #88034 | C23 | semidirect |
| 76. C2×#508 | D13 | semidirect |
| 107. #508 | C2×D13 | semidirect |
| 108. C2×Q32 | C2×D13 | semidirect |
| 114. C2×D16 | C2×D13 | semidirect |
| 145. Q32 | C22×D13 | semidirect |
| 151. D16 | C22×D13 | semidirect |
| 159. C2×C13 | #2263 | semidirect |
| 189. C13 | C2×#2263 | semidirect |
| 227. C2 | #13117148 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D208 | 2 |
| #13117148 | 2 |
| C2×#11718113 | 2 |
| C2×#11718111 | 2 |
| C2×#11718091 | 2 |
| C2×C13×#508 | 2 |
| C2×#2263 | 13 |