Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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. #13123101 | C2 | direct (N × H) |
| 2. C2×#11718610 | C2 | semidirect |
| 3. C2×#11718337 | C2 | semidirect |
| 4. C2×#11718655 | C2 | semidirect |
| 6. C2×C13×#399 | C2 | semidirect |
| 8. C22×C13×C4⋊C4 | C22 | semidirect |
| 13. C22×C4⋊Dic13 | C22 | semidirect |
| 14. C22×#6101 | C22 | semidirect |
| 15. C13×#399 | C22 | semidirect |
| 16. C2×C13×#95 | C22 | semidirect |
| 17. C2×#88071 | C22 | semidirect |
| 18. #11718655 | C22 | semidirect |
| 20. #11718610 | C22 | semidirect |
| 21. #11718337 | C22 | semidirect |
| 32. C2×C13×C4⋊C4 | C23 | semidirect |
| 42. C2×C4⋊Dic13 | C23 | semidirect |
| 44. C2×#6101 | C23 | semidirect |
| 45. C13×#95 | C23 | semidirect |
| 46. #88071 | C23 | semidirect |
| 82. C2×#399 | D13 | semidirect |
| 119. C22×C4⋊C4 | C2×D13 | semidirect |
| 125. #399 | C2×D13 | semidirect |
| 130. C2×#95 | C2×D13 | semidirect |
| 163. C2×C4⋊C4 | C22×D13 | semidirect |
| 173. #95 | C22×D13 | semidirect |
| 175. C2×C13 | #2842 | semidirect |
| 212. C13 | C2×#2842 | semidirect |
| 263. C2 | #13123101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13123101 | 2 |
| C2×#11718610 | 2 |
| C2×#11718337 | 2 |
| C2×#11718655 | 2 |
| C2×#11718616 | 2 |
| C2×C13×#399 | 2 |
| C2×#2842 | 13 |