Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 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 |
|---|---|---|
| 4. C2×#88117 | C2 | direct (N × H) |
| 6. C22×Q8×C13 | C4 | semidirect |
| 9. C2×Q8×D13 | C4 | semidirect |
| 14. C22×Dic26 | C4 | semidirect |
| 20. #88117 | C22 | direct (N × H) |
| 25. C2×Q8×C13 | C2×C4 | semidirect |
| 33. Q8×D13 | C2×C4 | semidirect |
| 44. C2×Dic26 | C2×C4 | semidirect |
| 59. Q8×C13 | C22×C4 | semidirect |
| 76. Dic26 | C22×C4 | semidirect |
| 82. C22×C13 | #103 | semidirect |
| 84. C2×D13 | #103 | semidirect |
| 102. C22×Q8 | #261 | semidirect |
| 112. C2×C13 | C2×#103 | semidirect |
| 114. D13 | C2×#103 | semidirect |
| 128. C2×Q8 | C2×#261 | semidirect |
| 146. C13 | C22×#103 | semidirect |
| 157. Q8 | C22×#261 | semidirect |
| 179. C22 | #88117 | direct (N × H) |
| 191. C2 | C2×#88117 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D13 | 2 |
| C22×C4⋊#261 | 2 |
| C22×D13⋊C8 | 2 |
| C2×#88117 | 2 |
| C22×#103 | 13 |