Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C13×Q16 | C2 | semidirect |
| 4. C2×#88076 | C2 | semidirect |
| 5. #11718853 | C2 | direct (N × H) |
| 6. C2×#88059 | C2 | semidirect |
| 12. C2×C13×Q16 | C22 | semidirect |
| 24. #88076 | C22 | semidirect |
| 25. #88059 | C22 | semidirect |
| 88. C22×Q16 | D13 | semidirect |
| 113. C2×Q16 | C2×D13 | semidirect |
| 126. C2×C13 | #473 | semidirect |
| 161. C13 | C2×#473 | semidirect |
| 205. C2 | #11718853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C2×#88196 | 2 |
| C2×#88155 | 2 |
| C2×#88076 | 2 |
| #11718853 | 2 |
| C2×#88059 | 2 |
| C2×#473 | 13 |