Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×D272 | C2 | semidirect |
| 2. C2×#11763046 | C2 | semidirect |
| 3. C2×#11762609 | C2 | semidirect |
| 4. C2×#11762588 | C2 | semidirect |
| 5. C17×#1380 | C2 | semidirect |
| 31. C2×D136 | D4 | semidirect |
| 39. C2×C16×C17 | D4 | semidirect |
| 41. C17×#107 | D4 | semidirect |
| 95. C22×D17 | D16 | semidirect |
| 121. #1380 | D17 | semidirect |
| 187. C2×C16 | D68 | semidirect |
| 189. #107 | D68 | semidirect |
| 191. C17 | #13304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| C2×#11763046 | 2 |
| C2×#11762609 | 2 |
| C2×#11762588 | 2 |
| C17×#1380 | 2 |
| #13304 | 17 |