Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1390 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1390 conjugacy classes of subgroups — too many to draw. Only its 280 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×#88098 | C2 | semidirect |
| 2. C22×#88103 | C2 | semidirect |
| 3. C2×#11718278 | C2 | direct (N × H) |
| 17. C2×#88103 | C22 | semidirect |
| 19. C2×#88098 | C22 | semidirect |
| 20. #11718278 | C22 | direct (N × H) |
| 52. #88103 | C23 | semidirect |
| 54. #88098 | C23 | semidirect |
| 152. C22×C13 | #361 | semidirect |
| 201. C2×C13 | C2×#361 | semidirect |
| 248. C13 | C22×#361 | semidirect |
| 291. C22 | #11718278 | direct (N × H) |
| 301. C2 | C2×#11718278 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88098 | 2 |
| C22×#88103 | 2 |
| C2×#11718278 | 2 |
| C22×D8×D13 | 2 |
| C22×#361 | 13 |