Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
422 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 84 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. #14545136 | C2 | semidirect |
| 4. #14544890 | C2 | semidirect |
| 5. #14543857 | C2 | semidirect |
| 6. #14543830 | C2 | semidirect |
| 27. #11762620 | C4 | semidirect |
| 28. #11762619 | C4 | semidirect |
| 29. #11762618 | C4 | semidirect |
| 30. C17×#360 | C4 | semidirect |
| 71. C17×M32 | C2×C4 | semidirect |
| 72. C17×#106 | C2×C4 | semidirect |
| 73. #10587488 | C2×C4 | semidirect |
| 74. #10587483 | C2×C4 | semidirect |
| 113. Q16×C17 | C4⋊C4 | semidirect |
| 115. D8×C17 | C4⋊C4 | semidirect |
| 125. Dic68 | C4⋊C4 | semidirect |
| 126. D136 | C4⋊C4 | semidirect |
| 227. #360 | #595 | semidirect |
| 267. M32 | C2×#595 | semidirect |
| 277. #106 | C2×#595 | semidirect |
| 285. C17 | #12943 | semidirect |
| 305. Q16 | C4⋊#595 | semidirect |
| 312. D8 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545538 | 2 |
| #14545136 | 2 |
| #14545092 | 2 |
| #14544890 | 2 |
| #14543857 | 2 |
| #14543830 | 2 |
| D17×#360 | 2 |
| #12943 | 17 |