Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #13117148 | C2 | semidirect |
| 2. #13117084 | C2 | semidirect |
| 3. #13116717 | C2 | semidirect |
| 4. #13113033 | C2 | semidirect |
| 5. #13113027 | C2 | semidirect |
| 6. #13113026 | C2 | semidirect |
| 7. C13×#2263 | C2 | semidirect |
| 29. C13×Q32 | D4 | semidirect |
| 33. C13×D16 | D4 | semidirect |
| 68. #2263 | D13 | semidirect |
| 123. Q32 | C22⋊D13 | semidirect |
| 130. D16 | C22⋊D13 | semidirect |
| 165. C13 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13117148 | 2 |
| #13117084 | 2 |
| #13116717 | 2 |
| #13113033 | 2 |
| #13113027 | 2 |
| #13113026 | 2 |
| C13×#2263 | 2 |
| #13692 | 13 |