Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2118 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2118 conjugacy classes of subgroups — too many to draw. Only its 587 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×#88173 | C2 | semidirect |
| 2. C2×#11718580 | C2 | direct (N × H) |
| 3. C22×#88068 | C2 | semidirect |
| 4. C22×D208 | C2 | semidirect |
| 5. C22×C16×D13 | C2 | semidirect |
| 6. C22×C13×Q32 | C2 | semidirect |
| 11. C2×#88173 | C22 | semidirect |
| 14. C2×C13×Q32 | C22 | semidirect |
| 16. C2×#88068 | C22 | semidirect |
| 18. #11718580 | C22 | direct (N × H) |
| 19. C2×D208 | C22 | semidirect |
| 20. C2×C16×D13 | C22 | semidirect |
| 34. #88173 | C23 | semidirect |
| 39. C13×Q32 | C23 | semidirect |
| 41. #88068 | C23 | semidirect |
| 43. D208 | C23 | semidirect |
| 44. C16×D13 | C23 | semidirect |
| 75. C22×Q32 | D13 | semidirect |
| 107. C2×Q32 | C2×D13 | semidirect |
| 113. C22×C13 | #508 | semidirect |
| 141. Q32 | C22×D13 | semidirect |
| 147. C2×C13 | C2×#508 | semidirect |
| 178. C13 | C22×#508 | semidirect |
| 203. C22 | #11718580 | direct (N × H) |
| 211. C2 | C2×#11718580 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88173 | 2 |
| C2×#11718580 | 2 |
| C22×#88068 | 2 |
| C22×D208 | 2 |
| C22×C16×D13 | 2 |
| C22×C13×Q32 | 2 |
| C22×#508 | 13 |