Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
600 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 258 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. C2×#88102 | C2 | direct (N × H) |
| 8. C22×C8×C13 | C4 | semidirect |
| 9. C22×#1055 | C4 | semidirect |
| 10. C2×C8×D13 | C4 | semidirect |
| 12. #88102 | C22 | direct (N × H) |
| 24. C2×C8×C13 | C2×C4 | semidirect |
| 25. C2×#1055 | C2×C4 | semidirect |
| 26. C8×D13 | C2×C4 | semidirect |
| 45. C8×C13 | C22×C4 | semidirect |
| 46. #1055 | C22×C4 | semidirect |
| 50. C22×C13 | #107 | semidirect |
| 52. C2×D13 | #107 | semidirect |
| 67. C22×C8 | #261 | semidirect |
| 71. C2×C13 | C2×#107 | semidirect |
| 73. D13 | C2×#107 | semidirect |
| 88. C2×C8 | C2×#261 | semidirect |
| 91. C13 | C22×#107 | semidirect |
| 109. C8 | C22×#261 | semidirect |
| 115. C22 | #88102 | direct (N × H) |
| 125. C2 | C2×#88102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#261 | 2 |
| C22×C8×D13 | 2 |
| C2×#88102 | 2 |
| C22×#107 | 13 |