Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88202 | C2 | semidirect |
| 3. C13×#417 | C2 | semidirect |
| 4. C2×#88063 | C2 | semidirect |
| 5. C2×#88049 | C2 | semidirect |
| 6. #11718150 | C2 | semidirect |
| 7. #11718122 | C2 | semidirect |
| 13. #88203 | C4 | semidirect |
| 100. #417 | D13 | semidirect |
| 187. C13 | #1907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88203 | 2 |
| C2×#88202 | 2 |
| C13×#417 | 2 |
| C2×#88063 | 2 |
| C2×#88049 | 2 |
| #11718150 | 2 |
| #11718122 | 2 |
| #1907 | 13 |