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×#11717439 | C2 | semidirect |
| 3. C2×#11716876 | C2 | semidirect |
| 4. #13104745 | C2 | direct (N × H) |
| 5. C2×#11716863 | C2 | semidirect |
| 6. C2×#11716860 | C2 | semidirect |
| 11. #11717439 | C22 | semidirect |
| 15. C2×C52×D8 | C4 | semidirect |
| 16. C2×#87810 | C4 | semidirect |
| 17. #11717232 | C4 | semidirect |
| 19. C2×#87802 | C4 | semidirect |
| 21. #11716876 | C22 | semidirect |
| 22. #11716863 | C22 | semidirect |
| 23. #11716860 | C22 | semidirect |
| 45. C52×D8 | C2×C4 | semidirect |
| 47. #87810 | C2×C4 | semidirect |
| 49. #87802 | C2×C4 | semidirect |
| 89. C2×C5×D8 | AGL(1,𝔽5) | semidirect |
| 131. C5×D8 | C2×AGL(1,𝔽5) | semidirect |
| 145. C2×C52 | #444 | semidirect |
| 177. C2×D8 | #1043 | semidirect |
| 189. C52 | C2×#444 | semidirect |
| 214. D8 | C2×#1043 | semidirect |
| 230. C2×C5 | #65733 | semidirect |
| 257. C5 | C2×#65733 | semidirect |
| 273. C2 | #13104745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717439 | 2 |
| C2×#11717232 | 2 |
| C2×#11716876 | 2 |
| #13104745 | 2 |
| C2×#11716863 | 2 |
| C2×#11716860 | 2 |
| C2×#65733 | 5 |