Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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×Dic104 | C2 | semidirect |
| 4. #13116928 | C2 | direct (N × H) |
| 5. C2×#11718084 | C2 | semidirect |
| 6. C2×C13×#366 | C2 | semidirect |
| 15. C2×Dic104 | C22 | semidirect |
| 20. C13×#366 | C22 | semidirect |
| 21. #11718084 | C22 | semidirect |
| 84. C2×#366 | D13 | semidirect |
| 89. C22×D13 | Q32 | semidirect |
| 124. #366 | C2×D13 | semidirect |
| 133. C2×D13 | C2×Q32 | semidirect |
| 166. C2×C13 | #2216 | semidirect |
| 202. C13 | C2×#2216 | semidirect |
| 243. C2 | #13116928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic104 | 2 |
| C22×C16×D13 | 2 |
| C2×#11718548 | 2 |
| #13116928 | 2 |
| C2×#11718084 | 2 |
| C2×C13×#366 | 2 |
| C2×#2216 | 13 |