Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 199 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. #14531066 | C2 | semidirect |
| 3. #14531065 | C2 | semidirect |
| 4. #14531064 | C2 | semidirect |
| 7. C17×#2254 | C2 | semidirect |
| 47. C16×D17 | Q8 | semidirect |
| 70. C16×C17 | C2×Q8 | semidirect |
| 71. #63214 | C2×Q8 | semidirect |
| 95. #2254 | D17 | direct (N × H) |
| 126. D17 | #2254 | direct (N × H) |
| 151. C17 | C2×#2254 | semidirect |
| 175. C16 | Q8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17×#500 | 2 |
| #14531066 | 2 |
| #14531065 | 2 |
| #14531064 | 2 |
| D17×#367 | 2 |
| C4×C16×D17 | 2 |
| C17×#2254 | 2 |
| C2×#2254 | 17 |