Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #13112907 | C2 | semidirect |
| 4. #13112800 | C2 | semidirect |
| 6. #13112753 | C2 | semidirect |
| 7. C8×C13×Q16 | C2 | semidirect |
| 36. #88068 | C8 | semidirect |
| 49. C13×Q16 | C2×C8 | semidirect |
| 68. #6090 | C2×C8 | semidirect |
| 70. C8×Q16 | D13 | semidirect |
| 153. Q16 | C8×D13 | semidirect |
| 173. C13 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#88068 | 2 |
| C8×D104 | 2 |
| #13112907 | 2 |
| #13112800 | 2 |
| #13112796 | 2 |
| #13112753 | 2 |
| C8×C13×Q16 | 2 |
| #12043 | 13 |