Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 3. #13117089 | C2 | semidirect |
| 4. #13117088 | C2 | semidirect |
| 5. #13117087 | C2 | semidirect |
| 7. C13×#2247 | C2 | semidirect |
| 86. #2247 | D13 | direct (N × H) |
| 98. C4×D13 | Q32 | semidirect |
| 129. C4×C13 | C2×Q32 | semidirect |
| 134. Dic13 | C2×Q32 | semidirect |
| 164. D13 | #2247 | direct (N × H) |
| 193. C13 | C2×#2247 | semidirect |
| 221. C4 | D13×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13×Q32 | 2 |
| D13×#494 | 2 |
| #13117089 | 2 |
| #13117088 | 2 |
| #13117087 | 2 |
| C4×C16×D13 | 2 |
| C13×#2247 | 2 |
| C2×#2247 | 13 |