Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11719098 | C2 | semidirect |
| 4. #11719092 | C2 | semidirect |
| 13. C2×C13×M16 | C4 | semidirect |
| 14. C2×#6099 | C4 | semidirect |
| 15. M16×D13 | C4 | semidirect |
| 17. C2×#6094 | C4 | semidirect |
| 19. #88102 | C22 | semidirect |
| 20. #88101 | C22 | semidirect |
| 39. C13×M16 | C2×C4 | semidirect |
| 40. C2×C8×C13 | C2×C4 | semidirect |
| 41. #6099 | C2×C4 | semidirect |
| 42. C2×#1055 | C2×C4 | semidirect |
| 43. #6094 | C2×C4 | semidirect |
| 44. C8×D13 | C2×C4 | semidirect |
| 101. C2×M16 | #261 | semidirect |
| 132. M16 | C2×#261 | semidirect |
| 136. C2×C8 | C2×#261 | semidirect |
| 143. C13 | #2911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88237 | 2 |
| C2×M16×D13 | 2 |
| #11719098 | 2 |
| #11719092 | 2 |
| #2911 | 13 |