Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1350 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 289 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 |
|---|---|---|
| 1. C2×D4×#3633 | C2 | semidirect |
| 2. #14545934 | C2 | semidirect |
| 3. #14545928 | C2 | semidirect |
| 4. C42×#3633 | C2 | semidirect |
| 32. C4×#3633 | D4 | semidirect |
| 33. C17×#127 | C8 | semidirect |
| 34. #10587626 | C8 | semidirect |
| 35. #10587560 | C8 | semidirect |
| 48. C2×D4×C17 | C2×C8 | semidirect |
| 49. C2×C22⋊D17 | C2×C8 | semidirect |
| 52. C2×D68 | C2×C8 | semidirect |
| 59. C42×C17 | C2×C8 | semidirect |
| 60. C4×Dic17 | C2×C8 | semidirect |
| 76. #3633 | #127 | direct (N × H) |
| 100. C4×C17 | C8×D4 | semidirect |
| 101. Dic17 | C8×D4 | semidirect |
| 126. #127 | #3633 | direct (N × H) |
| 138. C17 | C8×#127 | semidirect |
| 144. C2×D4 | C2×#3633 | semidirect |
| 162. C42 | C2×#3633 | semidirect |
| 197. C4 | D4×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#3633 | 2 |
| #14545934 | 2 |
| #14545928 | 2 |
| C42×#3633 | 2 |
| #127×#595 | 2 |
| C8×#127 | 17 |