Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×C13×Q16 | C2 | semidirect |
| 3. C2×#88069 | C2 | semidirect |
| 4. #11718840 | C2 | direct (N × H) |
| 5. C2×#88068 | C2 | semidirect |
| 6. C2×#88052 | C2 | semidirect |
| 12. C2×C13×Q16 | C22 | semidirect |
| 19. #88069 | C22 | semidirect |
| 20. #88068 | C22 | semidirect |
| 21. #88052 | C22 | semidirect |
| 71. C22×Q16 | D13 | semidirect |
| 94. C2×Q16 | C2×D13 | semidirect |
| 103. C2×C13 | #510 | semidirect |
| 131. C13 | C2×#510 | semidirect |
| 165. C2 | #11718840 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C2×#88158 | 2 |
| C2×#88069 | 2 |
| #11718840 | 2 |
| C2×#88068 | 2 |
| C2×#88052 | 2 |
| C2×#510 | 13 |