Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #14545833 | C2 | direct (N × H) |
| 36. C2×Q16×C17 | C8 | semidirect |
| 40. Q16×D17 | C8 | semidirect |
| 42. C2×Dic68 | C8 | semidirect |
| 82. Q16×C17 | C2×C8 | semidirect |
| 88. Dic68 | C2×C8 | semidirect |
| 161. C2×C17 | #1334 | semidirect |
| 163. D17 | #1334 | semidirect |
| 173. C2×Q16 | #3633 | semidirect |
| 198. C17 | C2×#1334 | semidirect |
| 216. Q16 | C2×#3633 | semidirect |
| 291. C2 | #14545833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763904 | 2 |
| C2×#11763898 | 2 |
| #14545833 | 2 |
| C2×Q16×#595 | 2 |
| C2×#1334 | 17 |