Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
498 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 498 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. #14545543 | C2 | semidirect |
| 2. #14545106 | C2 | semidirect |
| 3. #14545093 | C2 | semidirect |
| 4. #14544943 | C2 | semidirect |
| 5. #14543852 | C2 | semidirect |
| 6. #14543833 | C2 | semidirect |
| 24. C2×#10587499 | C4 | semidirect |
| 25. C2×D272 | C4 | semidirect |
| 26. C2×#10587497 | C4 | semidirect |
| 28. C2×C17×SD32 | C4 | semidirect |
| 38. C2×Q16×C17 | C2×C4 | semidirect |
| 51. C2×D136 | C2×C4 | semidirect |
| 66. C2×C16×C17 | C2×C4 | semidirect |
| 69. C2×#63214 | C2×C4 | semidirect |
| 196. C2×SD32 | #595 | semidirect |
| 224. C2×Q16 | C2×#595 | semidirect |
| 252. C2×C16 | C2×#595 | semidirect |
| 262. C17 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545543 | 2 |
| #14545106 | 2 |
| #14545093 | 2 |
| #14544943 | 2 |
| #14543852 | 2 |
| #14543833 | 2 |
| C2×#11763246 | 2 |
| #13033 | 17 |