Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
502 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 360 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. C2×#11763741 | C2 | direct (N × H) |
| 2. C22×#10587467 | C2 | semidirect |
| 4. #11763741 | C22 | direct (N × H) |
| 5. C2×#10587467 | C22 | semidirect |
| 21. #10587467 | C23 | semidirect |
| 51. C22×C17 | M64 | semidirect |
| 65. C2×C17 | C2×M64 | semidirect |
| 78. C17 | C22×M64 | semidirect |
| 104. C22 | #11763741 | direct (N × H) |
| 111. C2 | C2×#11763741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763741 | 2 |
| C22×#10587467 | 2 |
| C23×#63214 | 2 |
| C22×M64 | 17 |