Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#11718577 | C2 | semidirect |
| 2. #13125265 | C2 | semidirect |
| 3. #13125263 | C2 | semidirect |
| 4. #13117096 | C2 | semidirect |
| 5. #13117092 | C2 | semidirect |
| 6. #13117088 | C2 | semidirect |
| 7. #13117085 | C2 | semidirect |
| 8. C4×C16×D13 | C2 | semidirect |
| 9. C13×#2248 | C2 | semidirect |
| 77. C16×D13 | D4 | semidirect |
| 127. #2248 | D13 | semidirect |
| 195. C4×C13 | #508 | semidirect |
| 291. C13 | #33713 | semidirect |
| 333. C4 | #11718577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718577 | 2 |
| #13125265 | 2 |
| #13125263 | 2 |
| #13117096 | 2 |
| #13117092 | 2 |
| #13117088 | 2 |
| #13117085 | 2 |
| C4×C16×D13 | 2 |
| C13×#2248 | 2 |
| #33713 | 13 |