Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
450 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C16×#595 | C2 | semidirect |
| 4. #108×#595 | C2 | semidirect |
| 5. #14543847 | C2 | semidirect |
| 6. #14543846 | C2 | semidirect |
| 18. #11763724 | C4 | semidirect |
| 19. #11763723 | C4 | semidirect |
| 25. #11762617 | C4 | semidirect |
| 26. #11762616 | C4 | semidirect |
| 27. #11762615 | C4 | semidirect |
| 28. C17×#359 | C4 | semidirect |
| 53. #10587536 | C2×C4 | semidirect |
| 62. #10587529 | C2×C4 | semidirect |
| 63. C2×C16×C17 | C2×C4 | semidirect |
| 64. C17×#108 | C2×C4 | semidirect |
| 66. #10587490 | C2×C4 | semidirect |
| 67. C2×#63214 | C2×C4 | semidirect |
| 174. #595 | #359 | direct (N × H) |
| 199. #359 | #595 | direct (N × H) |
| 235. C2×C16 | C2×#595 | semidirect |
| 240. #108 | C2×#595 | semidirect |
| 249. C17 | C4×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#595 | 2 |
| D17⋊#359 | 2 |
| C2×C16×#595 | 2 |
| #108×#595 | 2 |
| #14543847 | 2 |
| #14543846 | 2 |
| D17×#359 | 2 |
| C4×#359 | 17 |