Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2062 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 331 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×#88074 | C2 | semidirect |
| 2. C2×#11718137 | C2 | direct (N × H) |
| 5. C23×D4×C13 | C4 | semidirect |
| 8. C2×C13×#127 | C4 | semidirect |
| 10. C22×C42×C13 | C4 | semidirect |
| 13. C2×#88074 | C22 | semidirect |
| 14. #11718137 | C22 | direct (N × H) |
| 26. C22×D4×C13 | C2×C4 | semidirect |
| 34. C13×#127 | C2×C4 | semidirect |
| 37. C2×C42×C13 | C2×C4 | semidirect |
| 41. #88074 | C23 | semidirect |
| 70. C2×D4×C13 | C22×C4 | semidirect |
| 82. C42×C13 | C22×C4 | semidirect |
| 127. C23×D4 | Dic13 | semidirect |
| 130. C2×#127 | Dic13 | semidirect |
| 133. C22×C42 | Dic13 | semidirect |
| 151. C22×C13 | #353 | semidirect |
| 170. C22×D4 | C2×Dic13 | semidirect |
| 178. #127 | C2×Dic13 | semidirect |
| 183. C2×C42 | C2×Dic13 | semidirect |
| 191. C2×C13 | C2×#353 | semidirect |
| 220. C2×D4 | C22×Dic13 | semidirect |
| 234. C42 | C22×Dic13 | semidirect |
| 235. C13 | C22×#353 | semidirect |
| 288. C22 | #11718137 | direct (N × H) |
| 301. C2 | C2×#11718137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88074 | 2 |
| C2×#11718137 | 2 |
| C22×C13×#127 | 2 |
| C22×#353 | 13 |