Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 82 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. #135×#595 | C2 | semidirect |
| 2. #14545106 | C2 | semidirect |
| 3. #14545098 | C2 | semidirect |
| 4. #14544935 | C2 | semidirect |
| 5. #14543865 | C2 | semidirect |
| 6. #14543827 | C2 | semidirect |
| 25. #11763250 | C4 | semidirect |
| 26. #11763247 | C4 | semidirect |
| 28. #11763244 | C4 | semidirect |
| 32. C17×#510 | C4 | semidirect |
| 45. C2×Q16×C17 | C2×C4 | semidirect |
| 59. C2×D136 | C2×C4 | semidirect |
| 77. C17×M32 | C2×C4 | semidirect |
| 82. #10587483 | C2×C4 | semidirect |
| 224. #510 | #595 | semidirect |
| 264. C2×Q16 | C2×#595 | semidirect |
| 291. M32 | C2×#595 | semidirect |
| 305. C17 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#595 | 2 |
| #14545106 | 2 |
| #14545098 | 2 |
| #14544935 | 2 |
| #14543865 | 2 |
| #14543827 | 2 |
| #14541919 | 2 |
| #13027 | 17 |