Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1470 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1470 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 |
|---|---|---|
| 1. C23×#63241 | C2 | semidirect |
| 2. C2×C22⋊#63241 | C2 | direct (N × H) |
| 5. C22×#63241 | C22 | semidirect |
| 6. C22⋊#63241 | C22 | direct (N × H) |
| 30. C2×#63241 | C23 | semidirect |
| 33. C24×C17 | C16 | semidirect |
| 62. C23×C17 | C2×C16 | semidirect |
| 85. C22×C17 | C22⋊C16 | semidirect |
| 88. C22×C17 | C22×C16 | semidirect |
| 105. C2×C17 | C2×C22⋊C16 | semidirect |
| 127. C17 | C22×C22⋊C16 | semidirect |
| 130. C24 | #63241 | semidirect |
| 157. C23 | C2×#63241 | semidirect |
| 178. C22 | C22⋊#63241 | direct (N × H) |
| 181. C22 | C22×#63241 | semidirect |
| 189. C2 | C2×C22⋊#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×C22⋊#63241 | 2 |
| C24×#3624 | 2 |
| C22×C22⋊C16 | 17 |