Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
242 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 80 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. #13131222 | C2 | semidirect |
| 2. #13129865 | C2 | semidirect |
| 3. #13129787 | C2 | semidirect |
| 4. C8×#6092 | C2 | semidirect |
| 49. #6092 | D8 | semidirect |
| 66. C8×C13 | M32 | semidirect |
| 128. C13 | #12039 | semidirect |
| 144. C8 | #88098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131222 | 2 |
| #13129865 | 2 |
| #13129787 | 2 |
| C8×#6092 | 2 |
| #13113630 | 2 |
| #12039 | 13 |