Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
758 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 113 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. #13125751 | C2 | semidirect |
| 2. C2×#11718734 | C2 | semidirect |
| 3. #13115676 | C2 | semidirect |
| 4. #13113504 | C2 | semidirect |
| 5. #13113287 | C2 | semidirect |
| 6. #13112674 | C2 | semidirect |
| 7. C13×#3151 | C2 | semidirect |
| 110. C13×M16 | D8 | semidirect |
| 128. #3151 | D13 | semidirect |
| 314. M16 | #6104 | semidirect |
| 328. C13 | #10144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125751 | 2 |
| C2×#11718734 | 2 |
| #13115676 | 2 |
| #13113504 | 2 |
| #13113287 | 2 |
| #13112674 | 2 |
| C13×#3151 | 2 |
| #10144 | 13 |