Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
942 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 509 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×#11763903 | C2 | direct (N × H) |
| 4. C22×#63241 | C4 | semidirect |
| 6. #11763903 | C22 | direct (N × H) |
| 20. C2×#63241 | C2×C4 | semidirect |
| 41. #63241 | C22×C4 | semidirect |
| 64. C22×C17 | #346 | semidirect |
| 82. C2×C17 | C2×#346 | semidirect |
| 100. C17 | C22×#346 | semidirect |
| 135. C22 | #11763903 | direct (N × H) |
| 145. C2 | C2×#11763903 | 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×#11763903 | 2 |
| C22×C4×#3624 | 2 |
| C22×#346 | 17 |