Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1858 conjugacy classes of subgroups; only the 414 normal subgroups are shown.
This group has 1858 conjugacy classes of subgroups — too many to draw. Only its 414 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 |
|---|---|---|
| 3. C2×#11716895 | C2 | semidirect |
| 4. #13104814 | C2 | direct (N × H) |
| 8. C2×#87862 | C4 | semidirect |
| 15. #11716895 | C22 | semidirect |
| 27. C2×#6034 | C2×C4 | semidirect |
| 29. #87862 | C2×C4 | semidirect |
| 55. #6034 | C22×C4 | semidirect |
| 78. C2×C5⋊D5 | #97 | semidirect |
| 122. C2×C52 | C2×#97 | semidirect |
| 125. C5⋊D5 | C2×#97 | semidirect |
| 173. C52 | C22×#97 | semidirect |
| 218. C2×C5 | #65676 | semidirect |
| 241. C5 | C2×#65676 | semidirect |
| 254. C2 | #13104814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#87862 | 2 |
| C2×C42×C5⋊D5 | 2 |
| C2×#11716895 | 2 |
| #13104814 | 2 |
| C2×#65676 | 5 |