Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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×#88117 | C2 | semidirect |
| 3. C2×#88115 | C2 | semidirect |
| 4. #11719136 | C2 | semidirect |
| 5. D13⋊(C22⋊C8) | C2 | semidirect |
| 6. C2×C13×#41 | C4 | semidirect |
| 9. C2×#6131 | C4 | semidirect |
| 12. C2×#6129 | C4 | semidirect |
| 16. C2×#6127 | C4 | semidirect |
| 93. Q8×C13 | C22⋊C4 | semidirect |
| 96. D4×C13 | C22⋊C4 | semidirect |
| 113. D52 | C22⋊C4 | semidirect |
| 125. Dic26 | C22⋊C4 | semidirect |
| 168. C2×#41 | #261 | semidirect |
| 239. C13 | #1788 | semidirect |
| 257. Q8 | C22⋊#261 | semidirect |
| 266. D4 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×D13 | 2 |
| C2×#88117 | 2 |
| C2×#88115 | 2 |
| #11719136 | 2 |
| D13⋊(C22⋊C8) | 2 |
| #1788 | 13 |