Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#88155 | C2 | semidirect |
| 3. C13×#408 | C2 | semidirect |
| 4. C2×#88077 | C2 | semidirect |
| 5. C2×#88065 | C2 | semidirect |
| 6. #11718150 | C2 | semidirect |
| 7. #11718142 | C2 | semidirect |
| 14. C2×#6107 | C4 | semidirect |
| 15. C2×#6106 | C4 | semidirect |
| 16. C2×#6105 | C4 | semidirect |
| 17. C2×#6104 | C4 | semidirect |
| 110. #408 | D13 | semidirect |
| 199. C13 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88204 | 2 |
| C2×#88155 | 2 |
| C13×#408 | 2 |
| C2×#88077 | 2 |
| C2×#88065 | 2 |
| #11718150 | 2 |
| #11718142 | 2 |
| #1876 | 13 |