Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 74 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. #14544959 | C2 | semidirect |
| 4. #14544207 | C2 | semidirect |
| 5. #14543645 | C2 | semidirect |
| 6. #14543634 | C2 | semidirect |
| 26. #11763201 | C4 | semidirect |
| 27. #11763169 | C4 | semidirect |
| 28. #11763168 | C4 | semidirect |
| 34. C17×#497 | C4 | semidirect |
| 49. C17×C4⋊Q8 | C2×C4 | semidirect |
| 67. #10587555 | C2×C4 | semidirect |
| 80. C17×#97 | C2×C4 | semidirect |
| 87. #10587474 | C2×C4 | semidirect |
| 239. #497 | #595 | semidirect |
| 279. C4⋊Q8 | C2×#595 | semidirect |
| 314. #97 | C2×#595 | semidirect |
| 323. C17 | #9379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545285 | 2 |
| #14544959 | 2 |
| #14544244 | 2 |
| #14544207 | 2 |
| #14543645 | 2 |
| #14543634 | 2 |
| #14539782 | 2 |
| #9379 | 17 |