Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 99 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×#11763076 | C2 | semidirect |
| 2. #14538428 | C2 | semidirect |
| 3. C2×#11762622 | C2 | semidirect |
| 4. #14530500 | C2 | semidirect |
| 5. C2×#11762592 | C2 | semidirect |
| 6. #14526880 | C2 | semidirect |
| 7. C22×C17×D16 | C2 | semidirect |
| 43. C2×D8×C17 | D4 | semidirect |
| 65. C2×C16×C17 | D4 | semidirect |
| 69. #10587490 | D4 | semidirect |
| 173. C22×D16 | D17 | semidirect |
| 246. C2×D8 | C22⋊D17 | semidirect |
| 267. C2×C16 | C22⋊D17 | semidirect |
| 274. C17 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763076 | 2 |
| #14538428 | 2 |
| C2×#11762622 | 2 |
| #14530500 | 2 |
| C2×#11762592 | 2 |
| #14526880 | 2 |
| C22×C17×D16 | 2 |
| #13319 | 17 |