Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 203 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×#88068 | C2 | semidirect |
| 3. C2×#11718852 | C2 | semidirect |
| 4. #13117098 | C2 | direct (N × H) |
| 5. C2×C16×Dic13 | C2 | semidirect |
| 6. C22×C13×Q32 | C2 | semidirect |
| 12. C2×C13×Q32 | C22 | semidirect |
| 15. #11718852 | C22 | semidirect |
| 17. C2×#88068 | C22 | semidirect |
| 22. C16×Dic13 | C22 | semidirect |
| 81. C22×Q32 | D13 | semidirect |
| 114. C2×Q32 | C2×D13 | semidirect |
| 163. C2×C13 | #2249 | semidirect |
| 197. C13 | C2×#2249 | semidirect |
| 232. C2 | #13117098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88068 | 2 |
| C22×D208 | 2 |
| C2×#11718852 | 2 |
| #13117098 | 2 |
| C2×C16×Dic13 | 2 |
| C22×C13×Q32 | 2 |
| C2×#2249 | 13 |