Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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. C4×C13×Q16 | C2 | semidirect |
| 2. C2×#88068 | C2 | semidirect |
| 4. #11718083 | C2 | semidirect |
| 5. C4⋊#6090 | C2 | semidirect |
| 21. C13×Q16 | D4 | semidirect |
| 50. C4×Q16 | D13 | semidirect |
| 60. C4×C13 | SD32 | semidirect |
| 82. Q16 | D52 | semidirect |
| 93. C13 | #2207 | semidirect |
| 116. C4 | #88068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×Q16 | 2 |
| C2×#88068 | 2 |
| #11718356 | 2 |
| #11718083 | 2 |
| C4⋊#6090 | 2 |
| #2207 | 13 |