Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1856 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 1856 conjugacy classes of subgroups — too many to draw. Only its 294 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×#11717441 | C2 | semidirect |
| 3. C2×#11716878 | C2 | semidirect |
| 4. #13104753 | C2 | direct (N × H) |
| 5. C2×#11716863 | C2 | semidirect |
| 6. C2×#11716860 | C2 | semidirect |
| 9. #11717441 | C22 | semidirect |
| 15. C2×C52×Q16 | C4 | semidirect |
| 16. C2×#87811 | C4 | semidirect |
| 17. #11717239 | C4 | semidirect |
| 19. C2×#87801 | C4 | semidirect |
| 21. #11716878 | C22 | semidirect |
| 22. #11716863 | C22 | semidirect |
| 23. #11716860 | C22 | semidirect |
| 45. C52×Q16 | C2×C4 | semidirect |
| 47. #87811 | C2×C4 | semidirect |
| 49. #87801 | C2×C4 | semidirect |
| 89. C2×C5×Q16 | AGL(1,𝔽5) | semidirect |
| 131. C5×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 144. C2×C52 | #444 | semidirect |
| 175. C2×Q16 | #1043 | semidirect |
| 189. C52 | C2×#444 | semidirect |
| 212. Q16 | C2×#1043 | semidirect |
| 229. C2×C5 | #65741 | semidirect |
| 257. C5 | C2×#65741 | semidirect |
| 273. C2 | #13104753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717441 | 2 |
| C2×#11717239 | 2 |
| C2×#11716878 | 2 |
| #13104753 | 2 |
| C2×#11716863 | 2 |
| C2×#11716860 | 2 |
| C2×#65741 | 5 |