Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C2×C13×C22⋊Q8 | C2 | semidirect |
| 2. C22×#6106 | C2 | semidirect |
| 4. C2×#88075 | C2 | semidirect |
| 5. C2×C22⋊#1055 | C2 | semidirect |
| 6. C2×#88049 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 36. C2×Q8×C13 | D4 | semidirect |
| 59. C13×C4⋊C4 | D4 | semidirect |
| 70. C2×#1055 | D4 | semidirect |
| 78. C23×C13 | SD16 | semidirect |
| 121. C2×C22⋊Q8 | D13 | semidirect |
| 193. C2×Q8 | C22⋊D13 | semidirect |
| 225. C4⋊C4 | C22⋊D13 | semidirect |
| 228. C13 | #2000 | semidirect |
| 242. C23 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C22⋊Q8 | 2 |
| C22×#6106 | 2 |
| C2×#88184 | 2 |
| C2×#88075 | 2 |
| C2×C22⋊#1055 | 2 |
| C2×#88049 | 2 |
| #11718121 | 2 |
| #2000 | 13 |