Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
862 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 469 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 |
|---|---|---|
| 2. C2×C4⋊#63241 | C2 | direct (N × H) |
| 6. C4⋊#63241 | C22 | direct (N × H) |
| 28. C22×C4×C17 | C16 | semidirect |
| 51. C2×C4×C17 | C2×C16 | semidirect |
| 67. C22×C17 | C4⋊C16 | semidirect |
| 72. C4×C17 | C22×C16 | semidirect |
| 85. C2×C17 | C2×C4⋊C16 | semidirect |
| 104. C17 | C22×C4⋊C16 | semidirect |
| 112. C22×C4 | #63241 | semidirect |
| 135. C2×C4 | C2×#63241 | semidirect |
| 141. C22 | C4⋊#63241 | direct (N × H) |
| 150. C4 | C22×#63241 | semidirect |
| 151. C2 | C2×C4⋊#63241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63241 | 2 |
| C2×C4⋊#63241 | 2 |
| C22×C4×#3624 | 2 |
| C22×C4⋊C16 | 17 |