Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11763855 | C2 | semidirect |
| 2. C2×#11763727 | C2 | semidirect |
| 3. C2×#11763726 | C2 | semidirect |
| 4. #14544933 | C2 | semidirect |
| 5. #14543849 | C2 | semidirect |
| 6. #14543824 | C2 | semidirect |
| 24. C2×#10587499 | C4 | semidirect |
| 25. C2×D272 | C4 | semidirect |
| 26. C2×#10587497 | C4 | semidirect |
| 28. C2×C17×SD32 | C4 | semidirect |
| 109. Q16×C17 | C22⋊C4 | semidirect |
| 121. D136 | C22⋊C4 | semidirect |
| 211. C2×SD32 | #595 | semidirect |
| 280. C17 | #13040 | semidirect |
| 301. Q16 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763855 | 2 |
| C2×#11763727 | 2 |
| C2×#11763726 | 2 |
| #14544933 | 2 |
| #14543849 | 2 |
| #14543824 | 2 |
| C2×#11763246 | 2 |
| #13040 | 17 |