Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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. #11719135 | C2 | semidirect |
| 3. #11719126 | C2 | semidirect |
| 4. #11718292 | C2 | semidirect |
| 5. C22×D4×C13 | C4 | semidirect |
| 13. #88192 | C4 | semidirect |
| 15. C2×C4⋊Dic13 | C4 | semidirect |
| 17. (C2×#261)⋊C4 | C22 | semidirect |
| 19. #88111 | C22 | semidirect |
| 101. C22×D4 | #261 | semidirect |
| 146. C13 | #1510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88192 | 2 |
| #11719135 | 2 |
| #11719126 | 2 |
| #11718292 | 2 |
| #1510 | 13 |