Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
342 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. C22×#88034 | C2 | semidirect |
| 3. #13112973 | C2 | direct (N × H) |
| 4. C22×C13×C32 | C2 | semidirect |
| 13. C2×C13×C32 | C22 | semidirect |
| 15. C2×#88034 | C22 | semidirect |
| 57. C22×C32 | D13 | semidirect |
| 62. C22×D13 | C32 | semidirect |
| 87. C2×C32 | C2×D13 | semidirect |
| 95. C2×D13 | C2×C32 | semidirect |
| 118. C2×C13 | C22⋊C32 | semidirect |
| 143. C13 | C2×C22⋊C32 | semidirect |
| 175. C2 | #13112973 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D13 | 2 |
| C22×#88034 | 2 |
| #13112973 | 2 |
| C22×C13×C32 | 2 |
| C2×C22⋊C32 | 13 |