Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
670 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 192 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. #14545181 | C2 | direct (N × H) |
| 18. C2×Dic136 | C4 | semidirect |
| 19. C2×#10587500 | C4 | semidirect |
| 20. Q32×D17 | C4 | semidirect |
| 23. C2×C17×Q32 | C4 | semidirect |
| 48. C17×Q32 | C2×C4 | semidirect |
| 50. #10587500 | C2×C4 | semidirect |
| 52. Dic136 | C2×C4 | semidirect |
| 141. C2×Q32 | #595 | semidirect |
| 152. C2×C17 | #2176 | semidirect |
| 154. D17 | #2176 | semidirect |
| 174. Q32 | C2×#595 | semidirect |
| 187. C17 | C2×#2176 | semidirect |
| 263. C2 | #14545181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#595 | 2 |
| #14545181 | 2 |
| C2×#11763736 | 2 |
| C2×#11763722 | 2 |
| C2×#11763696 | 2 |
| C2×Q32×D17 | 2 |
| C2×#2176 | 17 |