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. C22×D272 | C2 | semidirect |
| 2. C2×#11763079 | C2 | semidirect |
| 3. #14538432 | C2 | semidirect |
| 4. C2×#11762623 | C2 | semidirect |
| 5. #14530501 | C2 | semidirect |
| 6. #14526880 | C2 | semidirect |
| 7. C2×C17×#350 | C2 | semidirect |
| 61. C2×D136 | D4 | semidirect |
| 67. C2×C16×C17 | D4 | semidirect |
| 71. #10587490 | D4 | semidirect |
| 178. C2×#350 | 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 |
|---|---|
| C22×D272 | 2 |
| C2×#11763079 | 2 |
| #14538432 | 2 |
| C2×#11762623 | 2 |
| #14530501 | 2 |
| #14526880 | 2 |
| C2×C17×#350 | 2 |
| #13319 | 17 |