Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
494 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 1. #14545546 | C2 | semidirect |
| 2. D17⋊#359 | C2 | semidirect |
| 3. C2×#11763721 | C2 | semidirect |
| 4. #14544945 | C2 | semidirect |
| 5. #14543859 | C2 | semidirect |
| 6. #14543840 | C2 | semidirect |
| 24. #11763247 | C4 | semidirect |
| 26. #11763245 | C4 | semidirect |
| 27. #11763244 | C4 | semidirect |
| 32. C17×#509 | C4 | semidirect |
| 45. C2×D8×C17 | C2×C4 | semidirect |
| 59. C2×D136 | C2×C4 | semidirect |
| 77. C17×M32 | C2×C4 | semidirect |
| 82. #10587483 | C2×C4 | semidirect |
| 235. #509 | #595 | semidirect |
| 278. C2×D8 | C2×#595 | semidirect |
| 299. M32 | C2×#595 | semidirect |
| 315. C17 | #13022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545546 | 2 |
| D17⋊#359 | 2 |
| C2×#11763721 | 2 |
| #14544945 | 2 |
| #14543859 | 2 |
| #14543840 | 2 |
| D17×#509 | 2 |
| #13022 | 17 |