Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. #13131804 | C2 | semidirect |
| 2. C2×#11718275 | C2 | semidirect |
| 3. #13131151 | C2 | semidirect |
| 4. #13130724 | C2 | semidirect |
| 5. #13129913 | C2 | semidirect |
| 6. #13129902 | C2 | semidirect |
| 21. C13×#472 | C4 | semidirect |
| 23. #11718821 | C4 | semidirect |
| 24. #11718804 | C4 | semidirect |
| 25. #11718557 | C4 | semidirect |
| 216. #472 | #261 | semidirect |
| 370. C13 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131804 | 2 |
| C2×#11718275 | 2 |
| #13131151 | 2 |
| #13130724 | 2 |
| #13129913 | 2 |
| #13129902 | 2 |
| #13124554 | 2 |
| #13070 | 13 |