Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 228 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. C2×Q8×#261 | C2 | semidirect |
| 3. (C2×#261)⋊Q8 | C2 | semidirect |
| 6. C22×Q8×C13 | C4 | semidirect |
| 8. C2×Q8×D13 | C4 | semidirect |
| 9. C2×Q8×D13 | C4 | semidirect |
| 13. C22×Dic26 | C4 | semidirect |
| 43. C22⋊#261 | Q8 | direct (N × H) |
| 59. C2×#261 | C2×Q8 | semidirect |
| 61. Q8×C13 | C22⋊C4 | semidirect |
| 74. Dic26 | C22⋊C4 | semidirect |
| 82. C22×C13 | C4×Q8 | semidirect |
| 88. C2×D13 | C4×Q8 | semidirect |
| 105. C22×Q8 | #261 | semidirect |
| 146. C13 | Q8×C22⋊C4 | semidirect |
| 158. Q8 | C22⋊#261 | direct (N × H) |
| 186. C22 | Q8×#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D13 | 2 |
| C2×Q8×#261 | 2 |
| (C2×#261)⋊Q8 | 2 |
| #11719136 | 2 |
| C4×C22⋊#261 | 2 |
| Q8×C22⋊C4 | 13 |