Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
520 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 100 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. #13131643 | C2 | semidirect |
| 2. #13130133 | C2 | semidirect |
| 3. C2×#11718243 | C2 | semidirect |
| 4. #13130077 | C2 | semidirect |
| 5. #13129682 | C2 | semidirect |
| 6. #13129669 | C2 | semidirect |
| 100. C2×D52 | M16 | semidirect |
| 118. C13×M16 | M16 | semidirect |
| 339. M16 | #6118 | semidirect |
| 367. C13 | #9097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131643 | 2 |
| #13130133 | 2 |
| C2×#11718243 | 2 |
| #13130077 | 2 |
| #13129682 | 2 |
| #13129669 | 2 |
| #13123643 | 2 |
| #9097 | 13 |