Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
646 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 101 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. #13125754 | C2 | semidirect |
| 2. #13124302 | C2 | semidirect |
| 3. C2×#11718733 | C2 | semidirect |
| 4. #13113236 | C2 | semidirect |
| 5. #13113156 | C2 | semidirect |
| 6. #13112731 | C2 | semidirect |
| 7. C13×#1545 | C2 | semidirect |
| 111. C2×D52 | D8 | semidirect |
| 144. #1545 | D13 | semidirect |
| 371. C13 | #10176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125754 | 2 |
| #13124302 | 2 |
| C2×#11718733 | 2 |
| #13113236 | 2 |
| #13113156 | 2 |
| #13112731 | 2 |
| C13×#1545 | 2 |
| #10176 | 13 |