Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×#11763718 | C2 | semidirect |
| 2. C2×#11763716 | C2 | semidirect |
| 3. #14543913 | C2 | semidirect |
| 4. #14543911 | C2 | semidirect |
| 15. #11763201 | C4 | semidirect |
| 17. #11763196 | C4 | semidirect |
| 21. C4×#63223 | C4 | semidirect |
| 22. C17×#532 | C4 | semidirect |
| 28. C17×C4⋊Q8 | C2×C4 | semidirect |
| 29. C17×#127 | C2×C4 | semidirect |
| 57. #10587474 | C2×C4 | semidirect |
| 58. #10587474 | C2×C4 | semidirect |
| 177. #532 | #595 | semidirect |
| 216. C4⋊Q8 | C2×#595 | semidirect |
| 217. #127 | C2×#595 | semidirect |
| 236. C17 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763718 | 2 |
| C2×#11763716 | 2 |
| #14543913 | 2 |
| #14543911 | 2 |
| #14539252 | 2 |
| #13578 | 17 |