Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
498 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. M32×#595 | C2 | semidirect |
| 4. #108×#595 | C2 | semidirect |
| 5. #14543860 | C2 | semidirect |
| 6. #14543859 | C2 | semidirect |
| 19. #11763727 | C4 | semidirect |
| 26. #11762623 | C4 | semidirect |
| 27. #11762622 | C4 | semidirect |
| 28. #11762621 | C4 | semidirect |
| 29. C17×#361 | C4 | semidirect |
| 54. #10587535 | C2×C4 | semidirect |
| 63. #10587530 | C2×C4 | semidirect |
| 65. C17×M32 | C2×C4 | semidirect |
| 66. C17×#108 | C2×C4 | semidirect |
| 68. #10587490 | C2×C4 | semidirect |
| 69. #10587483 | C2×C4 | semidirect |
| 183. #595 | #361 | direct (N × H) |
| 206. #361 | #595 | direct (N × H) |
| 241. M32 | C2×#595 | semidirect |
| 248. #108 | C2×#595 | semidirect |
| 259. C17 | C4×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#595 | 2 |
| D17⋊#361 | 2 |
| M32×#595 | 2 |
| #108×#595 | 2 |
| #14543860 | 2 |
| #14543859 | 2 |
| D17×#361 | 2 |
| C4×#361 | 17 |