Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
690 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 106 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. #14544963 | C2 | semidirect |
| 3. #14544950 | C2 | semidirect |
| 5. #14543619 | C2 | semidirect |
| 6. #14543619 | C2 | semidirect |
| 24. #11763157 | C4 | semidirect |
| 25. #11763156 | C4 | semidirect |
| 26. #11763155 | C4 | semidirect |
| 30. C17×#486 | C4 | semidirect |
| 51. C17×C4⋊Q8 | C2×C4 | semidirect |
| 64. #10587555 | C2×C4 | semidirect |
| 74. C4×C8×C17 | C2×C4 | semidirect |
| 79. C4×#3622 | C2×C4 | semidirect |
| 269. #486 | #595 | semidirect |
| 305. C4⋊Q8 | C2×#595 | semidirect |
| 339. C4×C8 | C2×#595 | semidirect |
| 342. C17 | #9057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545314 | 2 |
| #14544963 | 2 |
| #14544950 | 2 |
| D17⋊#331 | 2 |
| #14543619 | 2 |
| D17×#486 | 2 |
| #9057 | 17 |