Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
618 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 618 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 |
|---|---|---|
| 2. #14543714 | C2 | direct (N × H) |
| 19. C22×Q8×C17 | C8 | semidirect |
| 49. C2×Q8×C17 | C2×C8 | semidirect |
| 152. C2×C17 | #1319 | semidirect |
| 161. C22×Q8 | #3624 | semidirect |
| 180. C17 | C2×#1319 | semidirect |
| 192. C2×Q8 | C2×#3624 | semidirect |
| 281. C2 | #14543714 | 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 |
| #14543714 | 2 |
| C2×#11762716 | 2 |
| C2×#1319 | 17 |