Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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. C42×#261 | C2 | semidirect |
| 4. C4×#6118 | C2 | semidirect |
| 5. #11718247 | C2 | semidirect |
| 11. C4×D4×C13 | C4 | semidirect |
| 12. D4×Dic13 | C4 | semidirect |
| 16. #88141 | C4 | semidirect |
| 20. C4×Dic26 | C4 | semidirect |
| 21. #88116 | C4 | direct (N × H) |
| 40. C4×#261 | C2×C4 | semidirect |
| 42. #6118 | C2×C4 | semidirect |
| 64. D4×C13 | C42 | semidirect |
| 83. Dic26 | C42 | semidirect |
| 100. C4×C13 | #104 | semidirect |
| 106. Dic13 | #104 | semidirect |
| 115. C4×D4 | #261 | semidirect |
| 164. C13 | C4×#104 | semidirect |
| 171. D4 | C4×#261 | semidirect |
| 207. C4 | #88116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6129 | 2 |
| C2×#88116 | 2 |
| C42×#261 | 2 |
| C4×#6118 | 2 |
| #11718247 | 2 |
| C4×#104 | 13 |