Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 219 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. #14531065 | C2 | direct (N × H) |
| 29. C2×C16×C17 | Q8 | semidirect |
| 37. C2×#63214 | Q8 | semidirect |
| 59. C16×C17 | C2×Q8 | semidirect |
| 60. #63214 | C2×Q8 | semidirect |
| 106. C2×C17 | #2254 | semidirect |
| 120. C2×C16 | Dic34 | semidirect |
| 129. C17 | C2×#2254 | semidirect |
| 150. C16 | C2×Dic34 | semidirect |
| 176. C2 | #14531065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763213 | 2 |
| #14531065 | 2 |
| C2×#11762637 | 2 |
| C2×#11762636 | 2 |
| C2×C16×Dic17 | 2 |
| C2×C17×#367 | 2 |
| C2×#2254 | 17 |