Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
242 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 76 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. #14544372 | C2 | semidirect |
| 3. #14543817 | C2 | semidirect |
| 4. #14543741 | C2 | semidirect |
| 6. C16×#3624 | C2 | semidirect |
| 43. #10587471 | C8 | semidirect |
| 62. Dic68 | C2×C8 | semidirect |
| 66. C16×C17 | C2×C8 | semidirect |
| 86. #3624 | SD32 | semidirect |
| 149. C17 | C8×SD32 | semidirect |
| 173. C16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544372 | 2 |
| #14544365 | 2 |
| #14543817 | 2 |
| #14543741 | 2 |
| #14543739 | 2 |
| C16×#3624 | 2 |
| #14530635 | 2 |
| C8×SD32 | 17 |