Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1858 conjugacy classes of subgroups; only the 534 normal subgroups are shown.
This group has 1858 conjugacy classes of subgroups — too many to draw. Only its 534 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 | direct (N × H) |
| 7. C22×#6034 | C4 | semidirect |
| 11. #11716895 | C22 | direct (N × H) |
| 21. C2×#6034 | C2×C4 | semidirect |
| 41. #6034 | C22×C4 | semidirect |
| 56. C22×C52 | #97 | semidirect |
| 92. C2×C52 | C2×#97 | semidirect |
| 131. C52 | C22×#97 | semidirect |
| 137. C22×C5 | #4002 | semidirect |
| 168. C2×C5 | C2×#4002 | semidirect |
| 186. C5 | C22×#4002 | semidirect |
| 187. C22 | #11716895 | direct (N × H) |
| 196. C2 | C2×#11716895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6034 | 2 |
| C22×C4×#1039 | 2 |
| C2×#11716895 | 2 |
| C22×#4002 | 5 |