Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
834 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 128 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×#11763654 | C2 | semidirect |
| 2. #14543712 | C2 | direct (N × H) |
| 6. #11763654 | C22 | semidirect |
| 20. C22×D4×C17 | C8 | semidirect |
| 57. C2×D4×C17 | C2×C8 | semidirect |
| 172. C2×C17 | #1318 | semidirect |
| 182. C22×D4 | #3624 | semidirect |
| 201. C17 | C2×#1318 | semidirect |
| 220. C2×D4 | C2×#3624 | semidirect |
| 321. C2 | #14543712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763654 | 2 |
| #14543712 | 2 |
| C2×#11762712 | 2 |
| C2×#1318 | 17 |